A maiden IPL 100 not out from Raina helped the Super Kings register 186 for four.
Super Kings had lost Wriddhiman Saha for 18 in the fourth over but Michael Hussey - 35 off 29 balls - and Raina combined for a 55-run second-wicket stand to steady the innings.
Albie Morkel made 23 off 16 deliveries as the hosts set an imposing target at the MA Chidambaram Stadium in Chennai.
Despite Shaun Marsh making 73 off 51 and David Miller's 26-ball 51, Punjab could only make 171 for six in response - which was largely due to Dwayne Bravo, who took 3 for 34 to ensure the win.
In the evening match Royal Challengers Bangalore proved too strong for the Pune Warriors, winning by 17 runs.
The top order all contributed as the visitors set 187 for three from their 20 overs, with an unbeaten 23-ball 52 from AB de Villiers the highlight.
In response Robin Uthappa put together a brave 45-ball 75, but the opener lacked support as his time fell behind the required run rate. Vinay Kumar bagged three wickets as the Pune innings subsided to 170 for nine from their 20 overs, solidifying RCB's place in the top four.