(idiomatic, intransitive) To start being in a winning position (e.g. in a race or competition).
After being neck-and-neck the whole race, Gibbs managed to pull ahead in the final lap.
He let the wagon pull ahead and crossed behind it, speeding up to reach the seat from the other side.
As fast as Kris ran, he couldn't catch her. He grew more baffled when she seemed to pull ahead of him without any sign of the exhaustion she'd showed when they stopped. Desperation could motivate, and so could fear for her sister. He pushed himself harder to catch her. Thunder boomed overhead. Forms he assumed were demons swooped above the canopy, casting shadows. He caught glimpses of fur and wings through leaves and ran until his chest was heaving. Hannah remained ahead of him, though he realized he was beginning to gain on her. He had to reach her before the demons did and swept her away, as they had Kiki.
While The Late Show initially won the ratings for the time slot against The Tonight Show with Jay Leno, in 1995, Leno's program began to pull ahead.
For music lovers, the Droid Incredible might pull ahead a bit when they compare the Droid Incredible vs. iPhone.
This is also the portion where the front-runner contestants pull ahead of the other entrants, so if you're planning to enter, be sure to put a lot of thought and creativity into your costume.