Fletcher made it seven goals in seven games after a first-half double which sealed victory against a spirited Saints side.
Both sides started the game positively with United having the best chance on 20 minutes when Joe Riley headed Josh Harrop’s free-kick over the bar.
Paul McGuinness’ men got the breakthrough six minutes later through the in-form Fletcher after a flurry of action in the area. A cross from the right was only half cleared by Saints’ stopper Harry Isted and after Harrop had clipped the post with a lovely curling effort, Riley saw his shot cleared off the line before Fletcher followed up to score from close-range.
Riley had a shot well saved soon, while Southampton striker Sam Gallagher sent a flying header just wide after rising to meet Dan Demkiv’s right-wing cross.
The Reds doubled the advantage on 37 minutes after a sweeping move. Harrop fired the ball out wide after great play in his own half. Having collected possession again and skipped into the area, his pin-point cross found Fletcher who couldn’t miss from three yards.
The visitors went close to pulling one back on the stroke of half-time when Gallagher took a pass on the run before evading two defenders and dragging the ball just wide, with Dean Henderson well beaten in the United goal.
Saints came out strongly after the restart with Jake Hesketh looping a shot just wide.