Both Liverpool and Tottenham have 55 points but Liverpool, which has played one more game, have a better goal difference. Fifth place secures a spot in next season's Europa League.
Rodriguez scored his fourth goal in two matches with a volley in the 10th minute, helped by a deflection off defender Danny Simpson.
Liverpool got a penalty in the 59th when Suarez went down after a challenge by Mike Williamson. Kuyt stepped up to score his eighth goal in seven Premier League matches.
In the 65th Suarez sidefooted under Newcastle goalkeeper Tim Krul for close-range for the third.
Resurgent Liverpool have now scored 14 goals in its last three home matches, including a hat trick from Rodriguez in the 5-0 demolition of Birmingham last week.
Suarez was a constant threat to the Magpies who have won only twice at Anfield in their last 39 visits. But Liverpool still required a slice of luck for its opener when John Flanagan's deep cross was only half headed clear by Williamson and Rodriguez's follow-up volley was heavily deflected by Simpson.
Kenny Dalglish's side relaxed and conceded too much territory to Newcastle, which enjoyed a sustained period of possession without threatening. Liverpool-born midfielder Joey Barton was the main culprit for Newcastle's lack of attacking prowess as his delivery from set-pieces was poor.
The one time he did put a free-kick into a dangerous area defender Glen Johnson headed behind for a corner, from which Kevin Nolan ballooned a shot over.
There was also a hint of fortune about Liverpool's second goal when Suarez isolated Williamson wide on the left from goalkeeper Jose Reina's kick and was sent tumbling by Williamson on the edge of the penalty area. Referee Peter Walton immediately pointed to the spot and Kuyt converted.
The Netherlands international should have doubled his tally with a free header seven yards out minutes later but missed the target.
Suarez made no such mistake when he exchanged passes with Kuyt to slip the ball under Krul from 10 yards.
With the game safe Dalglish sent on Andy Carroll for the final 20 minutes against his former club but the striker barely touched the ball.
Newcastle are 12th on 41 points.