Vokes’ last goal came in a 2-0 Championship win over Doncaster on March 25, four days before he ruptured his cruciate ligament.
Making only his second substitute appearance since, the striker produced a confident finish in the 73rd minute to cancel out Nacer Chadli’s 56th-minute opener and force a replay, with the winners to meet Leicester.
This was a repeat of the 1962 FA Cup final, won 3-1 by Spurs, and Burnley produced a special programme cover to mark the occasion.
Clarets manager Sean Dyche was given a boost ahead of the game with on-loan defender Michael Keane being permitted to play by his parent club Manchester United.
With captain Jason Shackell and his replacement Kevin Long both picking up injuries early in the 3-3 draw with Newcastle on New Year’s Day and Michael Duff still unavailable, Keane was Burnley’s only fit centre-half.
Ben Mee again deputised alongside Keane while Daniel Lafferty made his first start of the season at left-back.
Tottenham boss Mauricio Pochettino made seven changes from the team that stunned Chelsea, the starters including keeper Michel Vorm, midfielders Benjamin Stambouli and Paulinho and striker Roberto Soldado.
Fans had travelled in impressive numbers from north London but the home supporters were less enthusiastic, with only three stands open for the game.
The low-key atmosphere translated onto the pitch and neither side produced anything of real note during a distinctly lacklustre first half.
Tottenham enjoyed the majority of the possession but Burnley’s makeshift defence stood up very well and Tom Heaton’s goal was not threatened.
The only shot of the half came when Christian Eriksen picked out Paulinho on the edge of the box but his well-struck volley was blocked by Kieran Trippier.
Pochettino reacted at half-time by sending on free-scoring Harry Kane for Stambouli, who had picked up an early booking for pulling back Michael Kightly.
Spurs were more incisive from kick-off in the second half and Heaton was brought into the action by a header from Federico Fazio, but it was an easy save.
Down the other end, Danny Ings threatened for the first time when he cut in from the right and fired in a shot that Vorm fumbled before gathering at the second attempt.
But it was the visitors who opened the scoring in the 56th minute through Chadli.
Kane picked out Ben Davies on the left and his cross was controlled neatly by Chadli, who shot past Heaton with the aid of a deflection off Mee.
Spurs almost had a second moments later as Kane broke into the box but Heaton stood up to block his effort.
Dyche turned to his substitutes and sent on Vokes, who has had to be patient following a brief comeback appearance against Liverpool on Boxing Day.
Dyche left him out of the squad for the next two games, but now he had half an hour to impress and Burnley were beginning to exert more pressure.
One of their best moves saw George Boyd play in Dean Marney but his stabbed shot flew well over the bar.
They did not have to wait too long for an equaliser, though, and it was the moment Vokes has been waiting nine months for.
The striker was perfectly positioned in the centre of the box to guide Kightly’s cross into the far corner before being mobbed by his team-mates.
Tottenham came closest to a winner, with Mee blocking from Eriksen and Kane screwing wide, but they had to settle for a replay at White Hart Lane.