My understanding of the situation is that she feels that it's hard for you to say no, probably due to some sympathy and she uses that to exploit you. I'd say she does that just to make herself feel proud about how this woman swings guys to the left or to the right. Nothing criminal on the other hand, we all play this game without even noticing.
Some people just like to feel the advantage, i.e. friendship, business, work, family it's all the same - there's always a side with advantage and side with disadvantage. It's rare that two persons value each other equally, there's always side which overvalues and undervalues a mutual relation. It's all in our heads, the more you really value a person, the less value you emotionally produce for that person. It's like comparing a toy you already have with a toy that you want to get. So never expose your good or bad feelings it's always a loss for you.
In your case you obviously overvalue your friendship. Imagine yourself asking for the same favor a person who you really respect? Feels unreal right? That's because you value that person and your friend doesn't value you the same way like you value her.
So my advice would be:
First of all be positive about the situation itself, your final aim is gaining positive emotions for you and your friend.
Make your weak side your strong side, take advantage of communication, it's hard to come out with universal formula but if I were you I'd add some chilly to communication. It can always become subject for any kinds of discussions. It shouldn't be something that you care about it can be totally random joke. But be tolerant, elegant and respectful of what you say. For example I would extend the topic into uncomfortable zone and try to return it back to a person who was asking an uncomfortable question, making this person answer the harder question.
A good example in your case is a dating topic (or pick the one you like). So that the next time you see her, don't wait till she asks you for fixing her phone, ask her when she will be available for a fixing it. Demonstrate the fact that you're joking, put a smile on your face. Such strategy would allow you to start laughing at any point time and thus reducing the chance of being misunderstood to nearly zero. Also it will seamlessly change your image in your relations and show her that you're gaining your advantage back. There are plenty continuations for such communication, there should be couple rounds of jokes. If she picks time, make it explicitly understood that you joking about having a date with her at this time. If she asks to fix her phone right now you can say something like "Moment, babe, lemme take a shower first, I'll be back in 5 mins...". If she asks to download music suggest some romantic music. The list is infinite... All these tricks keep you on top of the communication thus demonstrate advantage, acting this way would make it simpler for you to say no to her.
The strategy is to make it hard for her to bounce your jokes back, after she fails to do so couple of times, she will feel her advantage diminished and you will be presented with choice to finish communication with something like "Ok, nice chat, see you around" and even if she asks you in such situation to fix her phone, it will be much easier for you to say "Sorry can't do, have a lot of stuff to do at home, let's do it next time".
I was originally expecting to drop just couple of lines, but ended with an opus, at least hope it was helpful, cheers!
The issue you guys raise in your comments it's all about choice, it's about who you decide to be. By saying "it'll be hard to pull off" I say It'll be even harder if you never try.
I remember one story related to this question. I once met my neighbours in an elevator and they had a daughter with them, she was 4-5 years old at that time and I said:
"Hey princess! You are so beautiful! Do you have a boyfriend already?"
and she said that she had two but she broke up with them because they didn't want to play with her in the sandbox. A funny thing to hear from a 5 y.o. which made me and their parents laughing. I responded that
"Then you need a new one, what if I would invite you to a date? Would you go to a date with me? Would you be my girlfriend?"
And she said that she will think about it which totally made a day for both me and her parents as all of us were laughing out of funny situation. Than later that day I had to visit those same neighbours to get back my tools they've previously took and as it turned out that my neighbour's mother (or grandmother) was visiting them and as I entered their home their daughter ran towards me and started talking loudly said that if I want her to be my girlfriend I need to make presents first and that it's better to start with ice-cream which made all laughing again. The grandmother (suppose the name is Alice) didn't had the context of the situation and I started explaining what happened in the elevator, and while explaining tried to switch the focus to my neighbours' mother to see how the reaction of daughter would change (suppose kid's name is Jenny). So I told:
"You see Mrs. Alice this is the way you loose a girlfriend, you decide to hang out with your friend to play your boy games and bang! You don't have a girlfriend. By the way since I've asked Jenny for a date and she didn't figured out yet whether she want's me as her boyfriend I think I can also ask you about the same thing would you happen to be free this evening? How would you feel for a date tonight?"
which made Mrs. Alice also laughing and she started saying something about that she wasn't on a date for more than 30 years already and she couldn't finish her phrase because small Jenny started loudly crying saying that grandmother is beating her boyfriends away. While all of the parents were trying to calm down small Jenny said that she don't need no gifts no ice-cream and want's to go to a date. Which was both totally awkward and funny but nevertheless instructive.
The moral of this story is that you can address the same joke to any age and even gender (but yeah, it should be appropriate though or at least wrapped accordingly). It works up until the point when you don't feel for what you say. If so it can be easily perceived as joke with no external effort.
And the second part of the moral (it doesn't come directly from story, but...) the grownups are also children with little more developed games and toys. If you try imagining a person you in front of you as a kid, you will address and treat this person accordingly. So It's all about how you perceive surrounding people. The state of dominance or suppression is based on your internal evaluation of a person. If you see your score lower than the person you are talking to, you would downgrade into submission, dominance otherwise.
Just know that having your score always high turns you into people-hating sociopath and low score makes you a submissive masochist beaten by everyone for no reason. Train to look at people under different angles. Improve your internal evaluation balance, seek for cooperation, respond with conflict for hostility.