At Home Park, the Pilgrims claimed a vital victory over Edgar Davids' Bees in front of a crowd of 8,210 but they remain in the bottom two.
Jake Hyde put Barnet ahead in the 21st minute but Argyle battled back, with Conor Hourihane levelling the scores at half-time before Ronan Murray fired the winner in the 49th minute.
York sacked manager Gary Mills following a home defeat by Bradford.
The beaten Capital One Cup finalists claimed a 2-0 win at Bootham Crescent thanks to second-half goals by James Hanson and Garry Thompson, with the result enough to draw the curtain on Mills' time at the club.
York have only claimed six out of a possible 33 points and the board of directors announced on the club's official website that they had terminated Mills' contract with immediate effect after the match.
Meanwhile, Gillingham remain at the top of the table even though they were unable to beat lowly Aldershot at the Recreation Ground.
The Gills came from behind to draw 1-1 after Craig Reid put Aldershot in front just after the break.
Leon Legge headed the equaliser for the visitors in the 75th minute to give them a three-point lead at the top over Port Vale, who dropped points themselves after they were beaten 2-1 by Oxford United.
Alfie Potter opened the scoring for the Us in the 10th minute but Doug Loft soon equalised for Vale to leave the scores tied 1-1 at half-time.
Deane Smalley gave Oxford the lead well into the second half before the home side wasted a chance to kill off the match when Sean Rigg missed an 84th minute penalty.
Third-placed Burton Albion crashed to a 3-0 defeat at Bristol Rovers, while Exeter's 3-0 home win over Northampton saw them close the gap to fourth place to a single point.
Rovers dominated their match with goals by Ryan Brunt, John O'Toole and Eliot Richards proving to be Burton's undoing.
Exeter, meanwhile, claimed the lead thanks to Lee Nicholls' own goal before scores by Jamie Cureton and Jake Gosling left them just outside of the play-off places.
Cheltenham remained in the play-offs thanks to a 2-1 home win over AFC Wimbledon, who lie bottom of the table.
Steve Elliott headed the opener before Darren Carter fired the second, with Brennan Dickenson's goal for Wimbledon not enough to change the outcome of the match.
Morecambe powered past Rochdale with goals from Chris McCready, Kevin Ellison and Andrew Fleming as they won 3-0 at the Globe Arena.
Southend and Rotherham drew 1-1, the Millers' Johnny Mullins cancelling out Kevan Hurst's 73rd-minute goal with an equaliser two minutes from full-time.
The match between Accrington and Torquay ended goalless while Anthony Stewart's 90th-minute header saw Wycombe edge past Fleetwood.
Chesterfield also won by a one-goal margin, Abu Ogogo's headed own goal enough to see them beat Dagenham & Redbridge 1-0.