Hodge smashed an unbeaten 48 off 21 deliveries as the home team successfully chased down a daunting target of 196 with two balls to spare.
It was glovesman Dishant Yagnik, playing his first match of the tournament, who hit successive boundaries off Dale Steyn to clinch the issue on a belter of a track at the Sawai Mansingh Stadium.
Royals required 25 runs in the last two overs and it became all the more difficult after Johan Botha was caught in the deep off Anand Rajan's first delivery of the penultimate over.
However, Hodge—who is the highest run-getter in the history of T20 cricket—had other ideas.
First, Hodge (6x4 2x6) smashed Anand Rajan to long-on for a boundary and then hit a magnificent six over wide long-off to bring down the equation to 11 in the last over.
First ball by Steyn was hit for two runs by Hodge before he gave the strike to Yagnik with a quick single.
Yagnik smacked the third ball past the off-side field and down to deep cover and then smashed the next delivery past the diving cover fielder to set off wild celebrations in the Rajasthan camp.
Earlier, Jean-Paul Duminy provided the late onslaught with an unbeaten 26-ball 58 after a solid opening stand as Chargers posted an imposing total.
After skipper Kumar Sangakkara (44) and Shikhar Dhawan (52) laid the platform with a 94-run opening stand, Duminy took the opposition bowlers to the cleaners, piling up 53 runs in the last three overs.
Duminy, playing his first match in IPL-V, struck five sixes, which included two off Pankaj Singh's penultimate over, and as many off Amit Singh's last over.