Rahane shared 113 runs with Nair, who made 61 off 38 balls, from just 11.3 overs for the second wicket as Rajasthan scored an imposing 189 for 2 after being put into bat at their second home venue at the Braboune Stadium.
Chasing the stiff target of 190, Delhi could only score 175 for 7 in 20 overs to lose the one-sided contest, which turns out to be IPL's 500th match.
The duo also capitalised on some sloppy fielding dished out by Delhi players as Rahane was dropped twice -- on 34 and 64 -- and Nair once -- on 35 . Delhi also conceded a few runs from sloppy ground fielding.
After today's win, Rajasthan, who have not won a single match in their last five encounters (three losses and no results), have 14 points from 11 matches to jump to the top of the league table, two more points than Chennai Super Kings who have played only nine games so far.
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The visiting side struggled throughout their run chase as they lost their first wicket at a total of 20 in the third over. They lost wickets at regular intervals and did not have a substantial partnership.
Captain Jean-Paul Duminy top-scored with a 39-ball 56 but none of his batting colleagues, including out of form Yuvraj Singh (22), gave him little support as Rajasthan won the match quite comfortably in the end.
Rajasthan captain Shane Watson (1/25 ) and James Faulkner (2/22) strangled the Delhi batsmen with some top class pace bowling. Stuart Binny and Dhawal Kulkarni also grabbed two wickets apiece.