Alan Pardew's side last achieved the feat in April 2012 and are riding on the crest of a wave, having moved up to sixth place in the top flight with a 2-1 win over West Brom on Saturday.
Yoan Gouffran scored for a third successive home game and Moussa Sissoko was also on target with a stunning long-range strike as the Tyneside outfit claimed their seventh Premier League win of the season.
Swansea did the double over Newcastle last term, so Pardew's charges will have a score to settle.
Gouffran has flourished despite playing wide on the left rather than in his more familiar role as a central striker and the France forward is determined to maintain his impressive form.
He told the club's official website: "Even though I'm playing on the left of midfield, I'm keeping my instincts of a striker.
"Every time I can get forward and try to score, I can, and that's what the manager is asking me to do.
"It was good to score again. Every time I score I'm happy, so it is no different. I'm so happy to be able to help the team win.
"It was a beautiful victory - a wonderful win - and it's done us so much good to get four consecutive wins."
Ryan Taylor is Newcastle's only absentee due to a knee injury and Pardew is unlikely to tinker with a winning side.
Swansea have won just one of their last eight games in all competitions after they were beaten 3-0 at Manchester City on Sunday.
Michael Laudrup's side are down in 13th in the table and they have only registered one league victory at the Liberty Stadium this season.
Laudrup felt the scoreline at the Etihad Stadium was not a fair reflection of the game and urged his players to be more ruthless.
The Dane could make changes as this will be Swansea's third game in six days, with winger Wayne Routledge pushing for a start against his former club.
Striker Wilfried Bony (hamstring) misses out, while Spanish duo Angel Rangel (calf) and Michu (ankle) are unlikely to feature.
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