Watson (101 runs off 61 balls) struck the first hundred of this IPL and propelled his team to 185 for four, before Hussey's 88 off 51 balls proved crucial in his team overcoming the stiff target in the 40th over.
Suresh Raina (51) contributed to the exciting win by scoring his first fifty of the competition.
The win pushed the two-time champions to top of the points table with 10 points from seven games while Rajasthan have four wins from seven matches, keeping them at fourth spot in the standings.
Chennai were cruising for victory, needing 32 off the last 24 balls and having six wickets in hand. But Hussey' run out and the back of Ravindra Jadeja in the 17th over spiced things up.
It became tricky or the home team when its skipper Mahendra Singh Dhoni (21) was caught at long-on off James Faulkner, leaving Dwayne Bravo and Chris Morris to get 11 off the last over.
Bravo (15 not out) delivered the knock out punch by hitting Watson over cover for a six. With a ball left in the match, it was yet another tense finish for the home side.
Earlier, Watson paced his innings to perfection for his first big score in the competition.
He was in attack mode from the ball one and took the team to 71 for no loss in seven overs. Ajinkya Rahane scored only 16 runs in the opening partnership before being bowled by Ravichandran Ashwin.
Chennai was able to restrict the flow of runs for a brief period until Watson cut loose again. He smashed the opposition bowlers all over the park with Ravindra Jadeja leaking the most number of runs, 45 from three overs.
Watson's memorable knock consisted of six huge hits and as many fours.
The Australian got out in the 18th over playing a tired shot. Stuart Binny (36 off 22) was settled at the crease by then and came up with the blows needed in the final few overs.