Liverpool climbed to second place in the standings, two points behind Arsenal, after Suarez added to Sturridge's contentious opening goal that came off his arm by scoring twice at the Stadium of Light.
After serving a 10-match ban for biting Chelsea defender Branislav Ivanovic during a league match in April, Suarez made his comeback in a frustrating League Cup loss to Manchester United on Wednesday.
He found the cutting edge against Sunderland, though, to help Liverpool earn a fourth win in six games and provide another demonstration of his burgeoning partnership with Sturridge that was cut short by Suarez's act of folly five months ago.
"He's getting the reward for his hard work over the period that he was off," Liverpool manager Brendan Rodgers said of Suarez. "Him and Daniel up front are a real, real handful. They combined very well."
Norwich beat Stoke 1-0 in Sunday's other match, with Jonny Howson scoring the winner from long range in the 34th minute to secure his team's second victory of the season.
Suarez couldn't have asked for more compliant opposition in his comeback match in the Premier League, with Sunderland having now lost five of its six games and being stranded at the foot of the table on just one point.
Interim manager Kevin Ball, who is in charge following the firing of Paolo Di Canio last weekend, was unable to shore up the league's leakiest defence in the face of one of the leading strike partnerships in English football.
Sturridge climbed to the top of the scoring charts with his fifth goal of the campaign, inadvertently bundling the ball in with his upper arm after misjudging the flight of Steven Gerrard's corner in the 28th minute.
Sturridge then turned provider, cutting in from the right and crossing for Suarez to poke in at the far post in the 36th. After Emanuele Giaccherini had halved the deficit in the 52nd, the same combination struck for Liverpool again to seal victory in the 89th, Sturridge making inroads down the left flank this time and crossing for Suarez to hook home a left-footed finish.
"It's great to have him back in, he gives us options and he's one of the best forwards in the league," Sturridge said of Suarez. "We form a good partnership."
Liverpool went above third-place Tottenham on goals scored and is now six points above arch-rival Man United, which sits in 12th place after losing 2-1 to West Bromwich Albion on Saturday.
United is level on seven points with Stoke and Norwich, who served up poor fare at Britannia Stadium except for Howson's brilliant effort that separated the sides.
"It was a disappointing performance and we were poor," said Stoke manager Mark Hughes, whose team outplayed Man City in its last home game. "We never got any pace or power into our game, which is unlike us."