The Hatters had recovered from a slow start by taking the lead through Asa Hall's second of the season in the 41st minute.
But Paul McManus headed his second of the campaign to level matters in the 76th minute.
Kevin Ellison, in hot form for Chester already this season, should have put his side ahead in the third minute when he ran clean through after indecision in the home defence, but Conrad Logan in the Luton goal smothered at his feet.
Eight minutes later and Ellison should have found the net again when Logan horribly miscued a free-kick on the edge of his own penalty area straight to the Blues frontman, but Ellison could only lob well wide from 50 yards with the goal at his mercy.
Ryan Lowe was the next to try his luck, seeing an 18-yard effort saved by Logan after Keith Keane had miscontrolled the ball in the 16th minute and three minutes later Ellison headed James Vaughan's right-wing cross just over the bar from eight yards.
Luton, who had looked nervy and short of confidence, finally mustered an attempt of sorts when Keane's 16-yard effort deflected up into the arms of John Danby after Chris Martin's lay-off in the 24th minute.
The hosts slowly improved and almost went ahead in the 35th minute when Hall neatly worked space on the edge of the area before drilling a low shot just past the post.
Six minutes later Hall went one better as he gave Luton the lead, thanks to superb endeavour from Claude Gnakpa down the right flank.
The full-back appeared too have over-run the ball as he made his way to the by-line past two defenders, but somehow managed to pull back for Jarvis to flick on to Hall to volley home powerfully from just inside the penalty area.
Gnakpa needed treatment after crashing into the advertising hoardings, but returned to his feet to a standing ovation from the home fans for his part in the goal.
Lifted by the goal, the Hatters started the second half brightly and Martin jinked his way past two challengers before driving a shot just past the far post from 15 yards in the 51st minute.
Ellison limped off on the hour, reducing the visitors' attacking threat and Luton almost netted again in the 64th minute when Michael Spillane's long ball released Marc Pugh, but with only Danby to beat he dinked his shot past the far post.
Chester rallied and substitute Anthony Barry almost made an immediate impact when his scorching 15-yard volley after a Lowe corner was superbly headed off the line by Keane in the 69th minute.
Seven minutes later the visitors were level when McManus - possibly the smallest man on the pitch - rose to head home Lowe's free-kick from seven yards out.
Keane saw a 20-yard volley palmed away by Danby in the 79th minute and Hall volleyed just wide in the 89th minute as Luton searched in vain for a winner.