The Raptors ended the Pacers' five-game winning streak in dramatic fashion, overcoming a four-point deficit during the final seconds of the fourth period.
Johnson tipped in a miss by Gay with 6.2 seconds left in the final quarter to bring the Raptors within two and Gay then stole an errant pass from Indiana's David West.
Johnson hurried a shot that missed, grabbed his own rebound and put it home to bring about a 90-90 tie.
Indiana's George Hill made 1-of-2 free throws with 1:30 left in overtime to tie it and neither side scored again until Gay hit a jumper with 1.7 seconds to go.
Toronto snapped a two-game skid and won on the road for just the sixth time in 25 tries this season.
Gay and DeMar DeRozan both scored 23 points for the Raptors. West led Indiana with 30 points. George added 26.