However, the Hammers' victory at Upton Park on Saturday was marred by the sending-off of Andy Carroll - who had set up both of Nolan's goals - shortly before the hour mark.
The hosts took the lead after 25 minutes. A long ball forward into the box was headed down by Carroll for Nolan, who controlled on his chest before crashing a superb volley into the net.
Their second came from a Stewart Downing corner in first-half stoppage time. The delivery towards the back post was headed by Carroll across the face of goal for Nolan to nod home from close range.
However, West Ham were reduced to 10 men in the second half when Carroll was sent off for what referee Howard Webb deemed to be an aggressive elbow to the face of Chico after an aerial tussle.
Replays suggested it might be a harsh decision but unless West Ham win an appeal, Carroll - who was making only his third start of the season - will miss their next three games.
The Hammers' victory was their first at home in the league since November 30 and briefly took them out of the drop zone, although they ended the day in 18th, behind West Brom on goal difference. Swansea are 12th, just two points better off.
Sam Allardyce made two enforced changes following the 0-0 draw at Chelsea. Defender George McCartney replaced Joey O'Brien (shoulder) and winger Matt Jarvis came in for Mohamed Diame (knee), while defender Winston Reid was on the bench and in line for a first appearance since November 2 following ankle surgery.
Swansea made three changes from the side which beat Fulham 2-0 in midweek, with Dwight Tiendalli, Jordi Amat and Nathan Dyer coming in, while new signing David Ngog was named on the bench.
The first time a meaningful string of passes was put together, there was a goal.
West Ham broke from deep and left-back McCartney drilled a cross into the area which Carroll stretched to reach.
His header found the late-arriving Nolan, who chested the ball down before volleying into the bottom corner.
It was a goal made in Newcastle in a link-up Allardyce has been desperate to see all season.
Swansea had an opportunity to respond when Jonjo Shelvey found Wilfred Bony with a bouncing ball.
James Tomkins, who was the last defender, had to time has challenge well and did so as Bony was waiting for the ball to drop for a shot.
Shelvey shot wide and Ashley Williams blasted over as Swansea again failed to test Adrian as they struggled to contain Carroll at the other end.
Carroll forced the corner which resulted in the second.
Downing's inswinging cross was met at the far post by Carroll, who craned his neck enough to direct the ball back into the six-yard box and Nolan headed it inside the post to double his tally for the season.
Shelvey had been marking the post, but the ball beat him.
Swansea clearly had not worked out how to deal with Carroll, whose participation came to an abrupt end.
Flores was climbing all over Carroll as they tangled in trying to meet an aerial ball near the halfway line.
As the striker threw the defender off his back, the Swansea man felt contact and went down theatrically.
Carroll was shown red by Webb, marched down the tunnel in disgust and Allardyce exchanged words with Flores on the touchline after the Spaniard had received treatment.
Flores and Webb were roundly booed thereafter.
Reid came off the bench, with Allardyce expecting a late onslaught from the visitors.
But Bony clipped substitute Alejandro Pozuelo's cross over and there was no late rally for Michael Laudrup's visitors as Upton Park celebrated a rare win and ensured Flores was aware of the scoreline.