The former Scunthorpe striker had headed the Hoops back into the lead just before the break after Johnny Russell had cancelled out Anthony Stokes' early opener.
Further goals from Ki Sung-yueng, Joe Ledley and James Forrest clinched the points in what turned out to be procession.
However, the Celtic boss, already without Glenn Loovens, Emilio Izaguirre and Beram Kayal through injury, watched in dismay in the 63rd minute as Hooper immediately signalled to the bench his distress following a challenge from United defender Paul Dixon.
Should the Englishman's injury prove to be as serious as it looked, it will give Lennon a problem ahead of Thursday's Europa League qualifying first-leg tie against side Sion.
However, on the form Celtic showed against United, he need not have any fears about the Swiss side.
The Taysiders, who had new signing Gavin Gunning on the bench, had not won at Celtic Park since Boxing Day 1992.
That record looked in little danger as the home side took the lead in the fourth minute after Dusan Pernis had made a mess of dealing with Kris Commons' long-distance drive.
The United goalkeeper dropped the ball and then had to concede a corner as he blocked from the onrushing Stokes.
When midfielder Ki crossed in to the box from the left, Hoops stopper Daniel Majstorovic got his head on to the ball and the former Hibernian striker forced it in from a couple of yards for his third goal in three SPL games.
As the game unfolded it became clear that the hint of danger in United's attacks were at odds with the air of uncertainty in their defence any time the ball came in to their box.
However, in the 31st minute, it was Celtic who failed to clear their lines and when United stopper Garry Kenneth played the ball across the box the unmarked Russell confidently knocked the ball past Lukasz Zaluska.
But the boost the visitors took from the goal lasted only two minutes.
As Celtic pressed United back in to their box, Mulgrew's cross was headed on to the bar by Stokes and Hooper was quickest to react to head in from a yard out when the ball fell out of the air.
While United tried to play in small triangles, the home side were slicker and more expansive although, at times, profligate.
For instance, Stokes tried to play a one-two with Mark Wilson in the United box when a shot on goal would surely have been more productive.
In the 53rd minute Commons found a yard of space in the Tannadice box and beat Pernis with a left-footed drive but the ball hit the far post and somehow stayed out.
But five minutes later, as Celtic broke with pace outnumbering the Tannadice defenders, Commons picked out Ki and he drove the ball high past Pernis from the edge of the box.
It was a simply-worked goal and one which appeared to have clinched the points but Celtic immediately switched off.
Moments later Zaluska appeared to get his hand onto a Kenneth header from Willo Flood's corner but referee Craig Thomson awarded a goal-kick.
Zaluska then made another good save, this time from Russell's close-range header with the Celtic defence again seemingly rattled.
But United almost paid the price again for pushing too many men forward.
Hooper raced past last defender Dixon on the break but fired wide from the edge of the box.
The Celtic striker immediately limped off - signalling he had been caught by the United defender - and was replaced by Shaun Maloney.
In the 71st minute, with United now in disarray, Maloney reached the byline before cutting back for Ledley to prod the ball in at the near post.
Maloney fired wide of the target when he only had Pernis to beat but in the first minute of injury time substitute Forrest, on for Commons, grabbed the fifth with a close-range drive, and with that Lennon's attention turned to Hooper.