Harry Smith's first-half goal put Cobblers in a strong position to qualify from Southern Group H in the Leasing.com Trophy after they beat Cambridge United 1-0 at the Abbey Stadium on Tuesday night.
Smith's toe-poke was the difference at half-time as Town played well in the first-half and then defended diligently in the second to take their points tally to five points from three games.
Cobblers have now finished their group stage campaign but will have to wait to discover their fate.
The only way they can be denied qualification to the knockout stage is if Cambridge beat both Peterborough and Arsenal Under-21s in their final two fixtures.
Jordan Turnbull returned from suspension and captained the side in one of five changes from Saturday, joined in the team by Andrew Fisher, Scott Pollock, Matty Warburton and Billy Waters.
Cobblers, perhaps keen to make amends for their defeat to Leyton Orient, made strong start at the Abbey Stadium and looked a real threat every time they crossed the halfway line.
Waters flashed a shot wide of the far post and neither Warburton nor Smith could force the ball home from close-range after United failed to clear Shaun McWilliams' cross.
Town moved into a deserved lead on 17 minutes when Reece Hall-Johnson picked up possession outside the box and weaved through several defenders before poking a pass to Smith, who stabbed under the onrushing Callum Burton and into the net.
Cambridge thought they had levelled but Andrew Dallas' effort was ruled out for a foul on Fisher and that moment apart, Town's defence coasted through the opening 45 minutes.
The rest of the half saw only half chances as Fisher comfortably saved from Greg Taylor and George Maris' free-kick struck the wall while Warburton slashed over for the Cobblers.
Fisher was called into much more strenuous action five minutes into the second-half when reacting brilliantly to palm away Sam Smith's shot from an indirect free-kick inside the box.
By and large though the Cobblers were untroubled as Curle sent on Alan McCormack and Morgan Roberts for McWilliams and Andy Williams.
United had a second effort chalked off, Harvey Knibbs this time denied by an earlier handball, and it was only in the last 10 minutes when Town's defending became a little desperate.
Harrison Dunk should have levelled when shooting against his own team-mate and Dallas then had two excellent chances to snatch a late leveller, first clearing the crossbar when through on goal before his 94th minute effort was tipped wide by a flying Fisher, which preserved victory for the visitors.
Cambridge: Burton, Taylor (c), Dallas, Maris, Dunk, John, Darling, Davies, Smith (Richards 66), Lewis, Worman (Knibbs 66)
Subs not used: Mitov, Knoyle, Taft, Simper, Ward
Cobblers: Fisher, Hall-Johnson, Turnbull (c), Wharton, Harriman, McWilliams (McCormack 67), Pollock, Warburton (Hoskins 82), Waters, Williams (Roberts 67), Smith.
Subs not used: Cornell, Hughes, Newell, Oliver
Referee: Sam Purkiss
Cobblers fans: 90