Left-hander Tewatia scored a 31-ball 53 as Rajasthan reached 226-6 in 19.3 overs. Tewatia's hitting upstaged Mayank Agarwal's first IPL hundred in Punjab's strong total of 223-2 after Rajasthan skipper Steve Smith won the toss and opted to field.
Smith (50) and Sanju Samson (85) scored brisk half centuries to keep Rajasthan in the hunt, but it was Tewatia's late onslaught which gave Rajasthan two victories from two IPL games.
Punjab has two points from three matches with their only victory coming against Royal Challengers Bangalore.
How to hit eight sixes in 11 balls
18th over - Rajasthan Royals needing 51 from 18 balls
6, 6, 6, 6, . , 6
19th over - Rajasthan Royals needing 21 from 12 balls
W, 6, 6, 1, 6, W