The home side had designs of moving onto the shoulders of sixth-placed Wisbech, but 16th-placed Town recorded a second successive away win to move within five points of a mid-table slot.
Town made the stronger start and created the game’s first chance when Tom Siddons forced a good save from home keeper James Goff, while Joe Braithwaite headed over from a corner.
Sileby also created a few early chances with Brian Farrell shooting wide and Mark Forbes firing over after a good cross from Joey Mann.
But at the other end Siddons went close again when he was denied by a goal-line clearance, while George Asplin had a shot blocked for a corner.
And on 26 minutes, Paul Ward’s side took the lead when Braithwaite took advantage of soem slack marking to bundle in George Asplin’s corner.
Brian Farrell had the first chance of the second half for Sileby, but his run into the box, after beating three players, came to nothing.
And within five minutes Town had doubled their lead when Siddons was left unmarked to head past Goff.
Forbes saw a free-kick saved for the hosts before Siddons scored his fourth goal in two games with a fine volley from inside the area.
Full-back Dan Worthington then hit the side-netting for Sleaford before Sileby had the ball in the net, only for Farrell to be denied by the linesman’s flag.
Sileby’s mood was further soured late on when Andy Hall was shown a straight red card.
Town have back-to-back games over the easter bank holiday weekend, starting with a trip to Wisbech on Good Friday.
Their penultimate game of the season follows on Monday when they host the derby clash with struggling Boston Town at Eslaforde Park (kick-off 3pm).