Sangakkara (60) and Pathan (39) shared a fifth wicket stand of 75 to enable Punjab to post 139 for six on a slow pitch.
Pathan then dismissed both Rajasthan openers in his first over and wicketkeeper Sangakkara held two catches as the Royals made a disastrous start, crashing to 42 for six.
Despite a seventh wicket stand of 60 between Ravindra Jadeja and captain Shane Warne, the defending champions were restricted to 112 for seven.
The win lifted Punjab to third place on the table after two successive wins.
Earlier, though, Punjab captain Yuvraj Singh must have wondered whether he made the right choice in deciding to bat as his side struggled to a precarious 48 for four after 8.2 overs.
Sri Lanka´s Sangakkara and fellow left-hander Pathan were the last two recognised batsmen and they batted responsibly to take their team to a respectable total.
Sangakkara made 60 off 51 balls while Pathan hit 39 off 33 deliveries.
Rajasthan´s top order batsmen failed again, with Swapnil Asnodkar playing a loose shot and Graeme Smith edging a good delivery from Pathan four balls later.
South African left-arm pace bowler Yusuf Abdulla also took two wickets in an over and Rajasthan´s chances virtually evaporated when Yusuf Pathan top-edged an attempted sweep against Piyush Chawla to be caught at short fine leg.
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