Jon Parkin's third goal in successive games beat Torquay and kept Fleetwood in touch with the play-off positions.
The striker headed in Dean Howell's cross for the only goal at Plainmoor.
But the Cod Army, who won for only the fourth time since Graham Alexander took charge at the start of December, needed keeper Scott Davies to be in top form.
Davies kept out efforts from Ashley Yeoman, Billy Bodin and Kevin Nicholson, while Gulls defender Aaron Downes hit the bar in stoppage time.
VIEWS FROM THE DRESSING ROOM
Torquay United assistant manager Shaun Taylor told BBC Radio Devon:
"I don't think we've had a better first half home or away all season, or even maybe last season. The effort from the players was fantastic, that's all I asked.
"I got a committed performance in the second half. They proved they're fit enough as they kept going until the end. But we're probably a bit disappointed with the final ball in the second half.
"Let's watch the TV tonight and see if those handball decisions are given, his hands are above him, your head should be there.
"We can feel sorry for ourselves but we've got to go again on Tuesday."
Fleetwood Town manager Graham Alexander told BBC Radio Lancashire:
"It was a tough game and we had to defend quite resolutely at times.
"Scott Davies made a couple of really good saves but we had opportunities ourselves. We're happy with a 1-0 away win.
"It's one thing you have to have - consistency in performances - and hopefully results follow that.
"It was a great header from Jon Parkin. He's a good player and just needs to get up to full match-fitness, but that will come with games."