A Kevin Nicholls penalty and a Rowan Vine cracker gave Mike Newell's men the victory and their first away win in ten games.
Yoann Folly and Leon Best made surprise debuts after Glenn Whelan had a virus and John Hills injured his hamstring during the game, causing a change-around from the manager.
Sturrock said: "In this league if you score the first goal you normally go on to win the game. We've paid fear for the chances we've created and not taken - we had some half-chances and some clear-cut ones that we didn't take.
"You have to give credit to Luton though. They play a very simple game with good strikers and width players. This leaves us with 21 points to get but now only 15 games to get them in."