But Jensen deserved equal billing for a superb penalty save to deny Michael Carrick an equaliser just before half-time.
Jensen then kept his cool during a tense second-half that United dominated, without ever looking likely to deny a team desperately trying to record their first top flight win since 1976.
Thirty-three years is a long time to wait. Yet the explosion of noise that greeted the final whistle at Turf Moor suggested it was all worthwhile as Owen Coyle carved another famous day in Burnley's history, and his own managerial career, coming out on top against fellow countryman Sir Alex Ferguson in such unexpected fashion.
As expected, Ferguson had rung the changes, recalling Carrick, Park Ji-sung and Anderson, as well as handing Michael Owen his first start.
The United boss was buoyed no doubt by Jonny Evans declaring himself fit to partner Wes Brown in central defence, which at least gave the Red Devils back line a more durable look.
Not that it seemed as though they would need it as Burnley rocked badly in the opening stages, struggling to get their bearings on a Turf Moor pitch which has waited so long to host top flight action.
Owen harshly had a goal ruled out for offside when he appeared to have timed his run onto Patrice Evra's through-ball to perfection before beating Jensen at the second attempt.
The former Liverpool star should have done better when Evra's left-wing cross flashed past him at the near-post and with Park, Carrick and Wayne Rooney all finding space, it seemed only a matter of time before United cruised to the front.
Yet the opening goal did not come. And as time ticked by, Burnley visibly gained in confidence.
Martin Paterson and record signing Steven Fletcher were both starting to cause problems when the Clarets launched a concerted raid on the visitors goal.
Paterson thought he was going to score when he sprang the United offside trap, only to find Ben Foster bearing down on him from the opposite direction.
The England goalkeeper made a brave block, then Carrick followed suit as Blake tried to turn home the rebound.
United could not relieve the pressure though and when former Manchester City full-back Stephen Jordan drifted a cross to the far-post, Blake was on hand to let fly with a superbly-struck volley which was past Foster before the United keeper had a chance to react.
A noisy crowd, raised the decibel level to ear-splitting proportions - but Coyle knew the job was not get done.
He knew exactly what to expect from the visitors, who recovered their poise and went after his team.
Yet, in front of Fabio Capello, Owen completely missed his intended header when Brown curled over a near-post cross which found England's fourth-highest goalscorer completely unmarked.
The odds must have been on Owen taking the penalty when Evra was upended by Blake as he nicked the ball towards Burnley's goal.
Instead, Carrick took responsibility - and Jensen emerged the hero, just as he did last season when his spot-kick saves turfed Chelsea out of the Carling Cup.
Jensen must have expected to be kept busy after the interval. But although United dominated possession, they had few clear-cut chances.
A long-range effort from Rooney that sailed harmlessly over was the best they could manage until Park created a bit of space for himself and forced Jensen into a fine full-length save, with Jordan hammering away the rebound.
By that time, Antonio Valencia and Dimitar Berbatov had been introduced; Owen making way after another disappointing contribution.
The pair made a difference. But Burnley were not to be denied, throwing themselves in the way of any United threat.
Jensen was a rock behind a sturdy defence and the final whistle ended a run of 17 straight wins for United against newly-promoted sides. More importantly, it marked Burnley's return to the elite - SOCCER NET