Sunderland sub Adam Johnson pulled one back to set up a nail biting final half an hour but the home side could not find another way through.
Carroll had opened the scoring in the ninth minute when his prodigous leap to meet Mark Noble’s corner was quite incredible and left the home defence watching on.
Things became a whole lot worse for the Black Cats in the 50th minute when Diame scuffed a shot past keeper Vito Mannone from 12 yards after Carroll chested the ball into his path.
Sunderland’s Johnson was a nuisance from the moment he arrived as a second half sub and grabbed a goal when Connor Wickham flicked a ball to Craig Gardner whose through ball was fired into the top corner by the substitute.
Fabio Borini saw a couple of chances go begging but Stewart Downing should have made it three earlier on when his great run ended with a shot trickling inches wide.
Boss Sam Allardyce punched the air at the end knowing that 37 points is almost certainly enough to ensure his team is playing Premier League football next season.
The booing this time came from the Sunderland fans giving their own team some grief!
And after all the moans of the last few days nobody was complaining about a generally very efficient Irons display