Dixon shook off a 10-grid spot penalty that relegated him to a 17th-place start, eventually overtaking Kimball and beating him to the finish line by 0.46 seconds.
It was the 30th career IndyCar win for Dixon and his first since August at Mid-Ohio.
Kimball's showing matched the best of his career while Dario Franchitti's third-place finish gave Gnassi Racing its first 1-2-3 finish ever in an IndyCar race.
Sunday's race was the first for IndyCar at the Pocono track since 1989.
Penske's Will Power took fourth place while Josef Newgarden rounded out the Top 5.