Paul Doswell's side came away from Hayes Lane with their third away win, already more than they achieved in all of last season - watch match highlights here.
Craig Eastman's single first-half goal was enough for Sutton, who climbed back to the top of the table, two points clear of second placed Dagenham and Redbridge.
Baird stepped in for post-match media duties, and told the club's website: "It's the first time I've realised Dos is lost for words! But being serious we're all really pleased and all the credit should go to the players because they've been absolutely outstanding.
"We've had plenty of injuries and the eleven who started the previous four games had played every minute of the season. We felt we needed to make changes and freshen things up. The players that have come in have been brilliant.
"In the first-half, our attacking performance was possibly the best of the season. The supporters may not appreciate it but the second half performance was completely professional in the way we broke the game up. They've been times when we'd have lost that 1-0 lead."