The Spitfires were pegged back twice by the visitors before Ben Williamson's last-gasp winner at the Silverlake Stadium.
The result sees them stay within touching distance of the U's in seventh place and extend their unbeaten home run to seven games.
Strevens told the club's website after the game: "We had a great belief and spirit to keep going forward, proved by our right wing-back flying forward, crossing the ball in and a diving header from the centre forward to win the game.
"That’s the sort of stuff fairy tales are made from.
You can see all the goals from Eastleigh's win against Sutton United by clicking here.
"The late goal was massive for us, it backs up the other two home games where we’ve won, including Harrogate who were in the play-offs, and now another against a top team.
"Hopefully the fans are seeing the boys care for the football club and want to play and do well.
"They’re fighting for each other and fighting for the club, long may that continue."