Harry Kane slotted past Petr Cech in the first half to give Mauricio Pochettino’s side a deserved lead against a Gunners team lacking any real spark in attack.
Olivier Giroud hit the crossbar with a second-half header and glanced another effort just wide, but Cech kept Arsenal in the match with fine saves to deny Toby Alderweireld and Christian Eriksen.
And the goalkeeper’s performance proved pivotal when substitute Gibbs converted Mesut Ozil’s cross at the far post 13 minutes from time to secure a share of the spoils for the home side.
Arsenal continue to trail Premier League leaders Manchester City on goal difference, while Spurs are back up to fifth in the table, five points adrift of their north London rivals.
Arsenal were on top in a scrappy opening 20 minutes, but both sides lacked any real composure in the final third, with early chances at a premium.
Eric Dier headed a good chance wide of the far post after Eriksen’s flighted free-kick as Spurs began to settle on the ball, and Danny Rose lashed over from 18 yards when given time and space.
Tottenham were in the ascendancy and Kane silenced the frustrated home fans after 32 minutes with his fifth goal in three league matches. The England striker’s simple run through the heart of the Arsenal defence was picked out by Rose’s long ball and he placed his effort past Cech into the far corner from inside the area.
Giroud went down under close attention from Jan Vertonghen off the ball and promptly barged the Belgium international to ground as tempers began to flare, before Cech denied Kane a second as he parried away a fierce low shot from the right of the area.
Arsenal came out flying in the second half and Joel Campbell had Hugo Lloris at full stretch with a curling effort after cutting in from the right, though Eriksen was inches from a Spurs second with a shot that clipped Mathieu Flamini’s knee and flew just wide.
Giroud then clipped the crossbar with a header from Ozil’s free-kick and Laurent Koscielny looped another header wide as the Gunners turned up the pressure in search of an equaliser.
Arsenal’s aerial threat looked their best chance of breaking down Spurs’ resistance and Giroud nodded Ozil’s corner wide of the far post when he rose unchallenged near the penalty spot.
Eriksen was thwarted by Cech with another good strike and Alderweireld’s header forced a strong parry from the former Chelsea star as Spurs looked for a killer second, but instead Arsenal grabbed an equaliser against the run of play through the most unlikely of sources.
Ozil clipped a cross towards the far post from the right and Gibbs, introduced off the bench just three minutes earlier, arrived in perfect time to sidefoot in at the near post for his first goal in over a year, despite Lloris’ best efforts to claw the ball off the line.
With their tails up, Arsenal pushed forward for a winner and Lloris did well to save Giroud’s glancing header low to his right, but Spurs held out to prolong their unbeaten run to 11 league matches.