Luton striker Steve Howard scored his sixth goal in three games but his side had to settle for a point against Stockport.
Howard netted with a trademark second-half header but Stockport skipper Dave Challinor cancelled it out eight minutes from time.
In the first half Luton struggled to break down a resolute Stockport rearguard and Howard became increasingly frustrated as he was repeatedly caught offside.
County midfielder Aaron Lescott had the game's first chance on five minutes when his first time side footed effort from Ali Gibb's cross drew a great save from Luton's rookie keeper Rob Beckwith.
Luton's best effort of the half came four minutes later when a good running cross from Peter Holmes saw top scorer Howard climb above his marker only to head narrowly wide from eight yards.
County then made four good chances in the space of five minutes, first Beckwith dived to his left to brilliantly turn Jim Goodwin's free kick behind for a corner. Then another Goodwin free-kick was flicked towards goal by Andy Welsh only for Beckwith to produce another fine stop.
Aaron Wilbraham then tested the Hatters keeper at his near post before Lescott sliced a good chance wide.
Luton took the lead on 61 minutes with what turned out to be their only on-target shot of the game.
Substitute Ahmet Brkovic crossed deep for Howard to power a header past Ola Tidman in the County goal.
Luton should have doubled their advantage on 70 minutes but striker Carl Griffiths prodded wide from just five yards.
They were made to pay on 82 minutes when Challinor was the first to react to a Jon Daly flick-on from a corner to head in the equaliser.
After the game Stockport Manager Carlton Palmer said: "I thought we totally dominated and were the best side throughout the game." Luton's boss Joe Kinnear said: "We needed that second goal. If Giffiths had scored it would have been all over."