The highly-rated midfielder's 34th-minute opener was complemented by Chris Morgan's header five minutes after the break and substitute Vincent Pericard's 71st-minute tap-in.
Jagielka's late second capped another precious victory for the Blades, who showed impressive fortitude to overpower the Hatters and reignite their promotion challenge after two successive draws.
The win edges them 13 points ahead of Luton, whose promising start to the season to the season is beginning to drain away.
The Hatters have now won just once in five games, and a trip to Bramall Lane was always going to be the acid test for Mike Newell's men.
But they did not disappoint during the early exchanges and generally matched United for the opening 45 minutes.
Indeed, just 18 seconds had passed when Luton winger Carlos Edwards carried the ball forward from the half-way line and hit a well-struck effort from 25 yards which warmed Paddy Kenny's hands.
United came back strongly two minutes later when Alan Quinn embarked on a scampering run which took him past a couple of visiting defenders and to the byline.
The speedy left-winger cut the ball back but Jagielka could only blaze his shot wildly over the bar from 12 yards.
Luton continued to press, however, and after nine minutes, Edwards flighted in a dangerous cross from the right which forced Morgan to head clear.
Five minutes later, Luton's vibrant approach almost saw them open the scoring when six-goal striker Steve Howard powered a firm goalwards, which again required Kenny to be alert.
But United began to pin the visitors back inside their own half and they claimed the all-important opening goal 11 minutes before the break.
Following a Quinn free-kick on the left flank, the ball found its way to Paul Ifill, whose effort was blocked, but Jagielka was on hand to rifle the ball home right-footed from six yards.
However, a minute before the break Luton were almost level when Kenny was forced to push Warren Feeney's shot out for a corner.
The Blades made the points safe five minutes after the break when Ifill was manhandled and Quinn flighted in the resulting free-kick which Morgan nodded home powerfully from 10 yards to register his first goal of the season.
The doughty visitors refused to give up but for all their effort and endeavour they were unable to find the end product.
And United took advantage with 19 minutes remaining when substitute Pericard fired home Derek Geary's low cross from the right as United eased to victory.
Jagielka's second of the night and fourth of the season came with two minutes remaining as he seized on a loose ball inside the visitors' box and rifled home from 15 yards to cap an impressive night's work.