Ok. This sort of question can go two different ways, so I'll address them both:
LEGAL PLAY:
In a Bo3. If you won the first game, but the game gets dragged out to where time is called and both players finish the final turn + 3 additional turns--and no winner has been determined, You would win as per the rules. I would highly recommend the guidelines for this.
ILLEGAL PLAY:
If an opponent is playing slow, CALL A JUDGE. It is illegal to run the clock. That said, some players aren't fast players, so it's up to you to figure out in game play "was my opponent playing fast in game one and won, and now they are playing rather sluggish". Watch for changes in gameplay. Make sure a judge watches gameplay between the both of you.
On the flip side, if a player is constantly hounding you to play faster, CALL A JUDGE. It is illegal to rush an opponent as well.
"Didn't you just say we should tell opponents to play faster for playing slow, but now we shouldn't tell them to go fast?"
There's a fine line between being reminded to speed up your plays, and then there's belligerant "c'mon, we're gonna tie! finish it up!" to deliberate attempts to fluster an opponent to get them to mess up in critical game points.