But Swansea failed to take advantage, losing out at Notts County. Mark Stallard got onto the end of a cross from David Pipe to seal the 1-0 win.
And it was Southend who did move up into the automatic promotion places, although they had to twice come from behind to earn a point at Chester.
Fredy Eastwood touched in a shot from Wayne Gray five minutes from time to seal a 2-2 draw.
Yeovil remain six points clear at the top, with Phil Jevons scoring from the spot after nine minutes for a 1-0 win over Leyton Orient.
United's win over Rushden leaves them trailing the Glovers, but re-opens a three point cushion ahead of fourth place.
A first-half hat-trick from Nathan Tyson inspired Wycombe to a 3-2 win over Lincoln at Sincil Bank, allowing Darlington to close the gap to the final play-off spot with a 1-0 home win over Boston United.
Kidderminster moved off the bottom of the table with a 1-0 win over Cheltenham, with John Mullins striking just after half-time.
Cambridge replace them as the worst team in the Football League, after a demoralising 2-1 loss at Bury.
New signing Iwan Roberts had fired the Us ahead after 28 minutes, but Jon Newby levelled for the Shakers and David Flitcroft hit a last-minute winner.
Oxford took the lead against Grimsby with a goal from Lucas Cominelli after 34 minutes, but debutant Matt Harrold inspired a turnaround for the Mariners after his introduction at half-time.
Harrold equalised within minutes of the restart, and Andy Parkinson grabbed the winner for the Cods.
Shrewsbury and Mansfield drew 1-1, and mid-table Bristol Rovers and Rochdale played out a 0-0 draw at the Memorial Stadium.