The Uruguayan striker was the focus of attention prior to kickoff at the Stadium of Light, as he prepared to make his first league start since biting Chelsea's Branislav Ivanovic five months ago.
However, it was strike-partner Daniel Sturridge who was surrounded by controversy after breaking the deadlock using his right arm.
Liverpool had the ball in the net moments later, as Martin Skrtel powered a rebound beyond Kieren Westwood, who had made a smart save top keep out Steven Gerrard's low free kick. However, the Slovak's effort was correctly ruled out for offside.
Sunderland looked threatening at the other end and Liverpool's crossbar was rattled midway through the half by a curling free kick from Larsson.
The home fans, who appear to have been rejuvenated following Kevin Ball's temporary appointment as manager, then appealed for a penalty as Emanuele Giaccherini went down under Kolo Toure's strong challenge. However, referee Howard Webb was correct to wave the appeals away.
Webb then made another big decision by allowing Sturridge's opening goal to stand on 28 minutes, despite the Liverpool forward knocking the ball over the line with his right arm following a set piece.
Sturridge's opener ended Liverpool's four-hour run without scoring a goal, but Reds fans had to wait just another eight minutes to see their side find the net again.
Suarez tapped home from close range following a brilliant run and cross by Sturridge.