With third-from-bottom Hull City in action 24 hours later 17th-placed Swansea moved four points clear of their rivals with goals by Fernando Llorente and Kyle Naughton.
Swansea can start planning for a seventh successive top-flight season if Hull lose to Crystal Palace on Sunday.
What could have been a tense afternoon against a side who did them an enormous favour by beating Hull last week turned into something of a cruise for the Welsh club.
Spaniard Llorente headed Swansea in front after nine minutes from Gylfi Sigurdsson's inch-perfect delivery.
Full back Naughton then hammered an angled piledriver past Jordan Pickford on the stroke of halftime.
Bottom club Sunderland's resistance was feeble throughout and they proved accommodating hosts as Paul Clement's Swansea picked up a third win in their last four matches.
Swansea were bottom of the league with 12 points when Clement took over on Jan. 3 following the sacking of Bob Bradley. Saturday's win took them to 38 points with a final home fixture against West Bromwich Albion to come.
Hull, who have two games left, have 34.
Clement is taking nothing for granted, though.
"It's a huge result for us. We've got ourselves into a strong position but the season is not over and we don't think it is done," he said. "Now have to look to next week.
"There's still one game to go. We'll be looking at the Crystal Palace and Hull game with a lot of interest but we can be happy with our work today.
"It was a bit of a messy second half but we got the job done."
Swathes of empty seats spoke volumes for the discontent among Sunderland fans.
Boos rang out, together with chants of "David Moyes out" at the final whistle.
"Everyone watching can see we need big changes. We need to alter the playing staff and I think everyone is aware of that," Sunderland manager Moyes said.
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