Steve Howard's thumping first-half header was enough to give Hatters three vital points with just five games remaining.
But they were thankful for some slack Seasiders finishing in the second half as the visitors forced Luton back.
Hosts Hatters started the brighter with first Peter Holmes heading Kevin Foley's right-wing cross just wide from 12 yards in the fifth minute and then Howard heading at Blackpool keeper Lee Jones from 15 yards a minute later after Rowan Vine's centre from the right.
Vine set up Howard to side-foot well wide from 16 yards in the 14th minute, but Town's leading scorer more than made amends a minute later by giving Hatters the lead with a thumping eight-yard header from Holmes' corner that gave Jones no chance.
As Luton dictated play, Foley was next to threaten in the 22nd minute when he went running into the penalty area from Ahmet Brkovic's clever backheel, but the full-back's cross-shot was held by Jones.
Howard then saw a shot blocked after a delightful move involving Holmes, Paul Underwood and Brkovic after half an hour, but Blackpool finally mustered an effort of note five minutes later when from Keigan Parker's corner, Rob Edwards got a touch on the ball to put off his team-mate John Murphy who headed wide from six yards.
Blackpool started the better after the interval and Parker raced clear in the 50th minute only to be hauled down by Sol Davis.
Davis looked to have been the last man, but referee Paul Armstrong awarded the Town defender just a yellow card.
Town finally woke up with a Vine shot blocked on the line by Clarke in the 58th minute and with a Howard header that flew just over a minute later from Underwood's in-swinging corner.
But Blackpool broke again when Parker fired just wide from 16 yards in the 63rd minute after Martin Bullock's pass from the right.
The visitors continued to press, prompting Town boss Mike Newell to hand new signing Warren Feeney his debut appearance as a 74th minute substitute for Vine.
Feeney almost found the net when he raced on to a superb 40 yard pass from fellow substitute Enoch Showunmi in the 83rd minute, but he dragged his shot just wide.
Instead Luton were thankful to Marlon Beresford's late save from Keith Southern four minutes from time as the home side hung on for three precious points.