Terry Bowes's 80th minute equaliser at The Hotel Ground cancelled out Emmerson Boyce's first half goal for Mike Newell's men, as both sides head for a replay at Kenilworth Road.
The Essex non-leaguers got off to a good start as David Collis and David Lee forced good saves from new Luton signing Marlon Beresford.
Colin McBride's men then had a case for a penalty when Thurrock's Cliff Akurang made a good run into the Luton box before he was dubiously bundled over by Ahmet Brkovic but referee Mike Thorpe waved away any claims for a spot kick.
Then, six minutes before the break, The Hatters took the lead against the run of play when a short corner saw Matthew Spring whip in a low near post cross which Boyce was able to knock in with his thigh to give the visitors a 1-0 lead.
Thurrock started the second half brightly through Akurang and Tresor Kandol and Collis went close with two chances, one a free kick that went just wide of Beresford's goal.
Then Kandol missed the home side's best chance of the match when Steve Heffer put him through on goal but his right foot strike went straight into the arms on the onrushing Beresford, when it appeared better to hit the shot with his left foot.
But Thurrock would not be denied as Bowes got on the end of substitute Paul Linger's pass to finish past Beresford and pull the non-leaguers level.
Kandol nearly made himself a Thurrock hero in the dying stages as he had another chance on goal but his attempted lob landed into the hands of Beresford, as both sides had to settle for the draw.
Click below for a match summary:
FA Cup
Thurrock 1-1 Luton
