However, the tall forward was sent off shortly after setting up Nolan's second early in the second half, following an innocuous looking clash with Chico Flores which left the Spaniard rolling theatrically on the Upton Park turf.
The 25-year-old faces a three-match ban if his appeal is not overturned, a loss which would hit West Ham's hopes of moving up to safety from 18th place.
"Hopefully we get justice in Andy's decision being overturned," midfielder Mark Noble told the club's official website (www.whufc.com).
"(Swansea manager) Michael Laudrup has come out on TV and said it wasn't a sending off, so that's good honesty from the man. If we can keep him and Kev firing together, with Jarvo (Matt Jarvis) and Stewart Downing producing crosses, hopefully we can stay solid and push up the table."
England's Carroll has recently returned to fitness, having missed the entire season since his 15 million pounds ($24.65 million) move due to ongoing foot injuries, leaving his side short of attacking options.
ATTACKING BOOST
Nolan's form has suffered as a result, and Noble said it was a boost to have the duo working together again.
"We did well on Saturday and with Kevin supporting off Andy, it works, it worked in the past and it's good to finally get them back together.
"That's what Kevin has got, that's what he has done his whole career, I don't know why everyone is so surprised. I know he hasn't got that many this year, but when he gets the chance he normally finishes it.
"You can see what effect Andy coming back had on him on Saturday."
As well as struggling in front of goal, West Ham have also been slack in defence, culminating in a humiliating 9-0 aggregate defeat over two legs to Manchester City in the League Cup semi-final.
Their woes at the back coincided with the loss to injury of Winston Reid, who helped his side to six clean sheets in their first 10 league matches.
The New Zealander made his return after a three-month layoff against Swansea, coming on with 11 minutes remaining to keep the opposition scoreless despite being a man down.
"The ankle's coming along." he said.
"I'm probably not 100 percent yet, as I've only just started training a couple of days ago. I think it was good for me to just go out there and feel that I was OK.
"I'm just trying to work hard, get back and get back to full fitness as quickly as possible."
($1 = 0.6085 pounds)
(Reporting By Josh Reich; Editing by John O'Brien)
