The Hoops had been humbled 3-0 at home to Juventus in the first leg of their Champions League last-16 tie on Tuesday night but responded well to losing a 10th-minute goal to Tannadice midfielder Stuart Armstrong to surge ahead through defender Efe Ambrose, Kris Commons and Joe Ledley.
At 2-1, Fraser Forster made a great save from a Jon Daly penalty, and Commons grabbed his second from the spot 10 minutes into the second half before Anthony Stokes notched a double to complete the rout, with Johnny Russell scoring late on for the Taysiders.
The Green Brigade, the most raucous and militant section of the home support, had boycotted the game as a protest against Strathclyde Police, it was rumoured, and they missed one of the better league games this season which ended with Celtic 18 points clear of Motherwell at the top of the table.
Lennon made three changes following his side's exertions against Juve with Adam Matthews and Ledley coming in for defender Mikael Lustig and skipper Scott Brown, out with respective thigh and abductor injuries, while Stokes replaced James Forrest who started on the bench.
United, managed by former Hoops defender Jackie McNamara who was looking to make it three wins out of three since taking over at Tannadice, made one change with defender Brian McLean in for Gavin Gunning, ruled out with a knee injury.
The visitors did not look cowed in the early stages, despite the fact that they had have not won away to Celtic since Boxing Day 1992.
United appeared to take a step towards ending that dreadful run when Mackay-Steven robbed Charlie Mulgrew near the touchline and sped towards goal before playing in Armstrong, who did not break stride before drilling his shot low past Fraser Forster and into the far corner.
However, the small knot of travelling fans barely had time to celebrate as a minute later Ambrose powered in a header from a Commons corner, before treating the Celtic support to an impressively acrobatic celebration. Lennon's men hardly looked back.
Left-back Emilio Izaguirre was the architect of Celtic's second goal in the 21st minute when his cross from the left ended up at the feet of Commons, who controlled the ball before hammering it past the helpless Radoslaw Cierzniak.
Forster then made a fine block from Keith Watson's header from a Barry Douglas free-kick but the England call-up made an even better save when United were controversially awarded a spot-kick in the 25th minute.
Matthews appeared to tackle Mackay-Steven cleanly with most in the stadium anticipating a corner but referee Bobby Madden enraged the home support - and looked to have surprised the United players - when he pointed to the spot before booking Matthews and the protesting Forster.
Jeers of derision for the official turned to cheers when Forster threw himself to his right to parry Daly's penalty and with that setback, United appeared to crumble.
There was suggestions that the penalty had been awarded for a pull on Mackay-Steven's shirt, the irony of which, would not have been lost on Lennon.
The Northern Irishman revealed yesterday that Celtic would be seeking "clarification" over Spanish referee Alberto Undiano Mallenco's performance during the defeat by Juventus when he allowed some blatant manhandling of the Hoops players to go unpunished.
Celtic piled forward with pace and purpose and in the 37th minute, another spell of pressure ended when Ledley's deflected shot from 16 yards ended up behind the hapless Cierzniak.
United started the second half positively and in the 51st minute Izaguirre blocked a Brian McLean header from a Douglas corner while standing on the line, but Celtic raced up the park and Gary Hooper screwed a drive from 16 yards just wide of the far post.
There was no stopping the champions though.
Commons made it 4-1 from the spot in the 55th minute after Douglas was adjudged to have fouled Stokes, although the Irishman placed it on the spot to take it himself before making way for the Scotland international.
The home fans were enjoying themselves but moments later they had Forrest to thank again when he blocked an effort from Mackay-Steven after the pacy United player had outstripped Celtic defender Kelvin Wilson.
There were no shortage of goalmouth incidents as United capitulated.
Stokes, clearly desperate to get on the scoresheet, drew a good save from Cierzniak with his long-range drive before Mulgrew clipped Common's pass from a free-kick over the bar.
The Parkhead men continued to create chances and Stokes eventually got the goal he was looking for in the 71st minute when he hammered a drive from the edge of the box past Cierzniak.
Stokes doubled his tally in the 82nd minute after Cierzniak had parried a header from James Forrest, on for Victor Wanyama, leaving the former Hibernian player to slam into the net from six yards.
In the final seconds Russell grabbed a goal for United after forging his way into the Celtic box but it was not even a consolation for the pulverised visitors.
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