The Hatters enjoyed the better of the game in the opening minutes as Darlington's on-loan keeper Dean Gerken was called into action.
The Colchester man's poor clearance after only 90 seconds gave an early opportunity to Ian Henderson, who was off-target with a 20-yard low drive.
Two minutes later Gerken was in the right place to smother a shot from Rossi Jarvis as the visitors threatened an early breakthrough.
The hosts had a goal ruled out after eight minutes when Liam Hatch was ruled offside, but seconds later Darlington took the lead when Rob Purdie was tripped inside the area and the midfielder picked himself up to send Conrad Logan the wrong way from the spot.
Worse was to come for the visitors when Hatch produced two goals in three minutes to put the home side in full control.
Hatch's first came from a well placed header to convert Purdie's corner in the 24th minute and then two minutes later when an Alan White header came back off the bar, Hatch was in position to slot in his side's third goal of the game.
A mix-up in the Luton defence left Darlo full-back Neil Austin with a simple chance for the fourth in the 28th minute and this extraordinary game took another turn when Chris Martin pulled a goal back with a sweet volley on the half-hour mark to give Town a bit of hope.
In the second half Darlington had further chances to increase their advantage, but Purdie and Pawel Abbott were denied by goal-line clearances from George Beavan in the 55th minute.
Purdie then had a shot tipped over the bar by Logan in the 72nd minute, before substitute Gregg Blundell raced on to a pass from Abbott to steer the ball under the exposed Logan five minutes from time.