The Royals, who are in third spot but are reeling from spot-fixing allegations, made it six home wins out of seven in what could prove to be a vital victory in the play-off shake-up.
Sunrisers move ahead of Royal Challengers Bangalore with one match remaining.
The Hyderabad-based side play third-bottom Kolkata Knight Riders in their last match of the regular season, while Bangalore face second-placed Chennai Super Kings.
Royals may have already sealed their play-off place but with former India Test bowler Shanthakumaran Sreesanth, Ankeet Chavan and Ajit Chandila all questioned by police and immediately suspended, it could be a difficult few weeks ahead.
Royals were nonetheless chasing second place, and they started well enough by restricting the Sunrisers to 137, with James Faulkner taking five wickets for 16 runs in four overs.
But a terrible chase saw them manage just 113 for 9 thanks to some economical bowling from the likes of Dale Steyn (4-0-8-2), slumping to a defeat that – while making little difference in qualification terms – will hardly boost confidence ahead of the play-offs.