The West Ham captain's first-half double earned the points for Sam Allardyce's side, who played the final half an hour with a numerical disadvantage after Andy Carroll marked his first home top-flight start of the season with a straight red card following a challenge with Chico Flores.
Carroll assisted both of Nolan's goals with typically adept knock-downs, but his game was cut short when referee Howard Webb dismissed the striker after an aerial challenge with Flores resulted in his flailing arm clipping the Spaniard's head.
However, despite that setback, West Ham stood firm in the face of continued Swansea pressure to record just their third Premier League win of the season at Upton Park and go above Stoke City on goal difference ahead of their match against Manchester United.
Both clubs were active in the January transfer window, but all three new signings named in their squads on Saturday started on the bench.
Italian duo Marco Borriello and Antonio Nocerino were among West Ham's substitutes, while Swansea manager Michael Laudrup kept David N'Gog in reserve.
The hosts started the brighter, and had the first chance of the game when Carroll headed Matt Jarvis' cross wide after six minutes.
Allardyce's men continued probing, and deservedly took the lead through Nolan's well-taken 27th-minute strike.
The skipper still had plenty to do after the unmarked Carroll nodded down Matt Taylor's delivery, but he took a touch before expertly volleying home from just inside the area with his left foot.
Swansea responded well to going behind, but failed to test home keeper Adrian and were made to pay on the stroke of half-time as West Ham's tried-and-trusted method of Nolan feeding off Carroll's knock-downs bore fruit once again.
More lacklustre marking from Swansea was punished, as they again failed to pick up Carroll, who nodded Stewart Downing’s corner back across goal for Nolan to divert a close-range header beyond the helpless Gerhard Tremmel.
The home side picked up where they left off after the interval, and Jarvis rounded Tremmel before seeing his cross hacked clear by Ben Davies.
However, the pattern of the game was turned on its head when Webb had no hesitation in dismissing England international Carroll for his part in the seemingly innocuous incident with Flores.
Inevitably, Swansea then began controlling the game but struggled to force Adrian into action as West Ham dropped deeper.
But despite their territorial dominance, Laudrup's side - who are now winless in six league games away from home - were impotent in attack, with Wilfried Bony spurning their only real chance by volleying over the bar 10 minutes from time.
West Ham, who introduced Nocerino for match-winner Nolan in the closing stages, were able to hold on relatively comfortably to record their 11th Premier League clean sheet of the campaign - the most shutouts in the division.
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