When Gary Hooper scored his second goal in the 49th minute - after Jambos midfielder David Obua had been sent off by referee Craig Thomson before the break for raising a hand to Charlie Mulgrew
- a supporter came out the main stand to grapple with the Parkhead boss.
An astonishing melee ensued and the intruder was eventually marched up the tunnel by police but that was not the end of the trouble as some fans in the Celtic section of the ground appeared to fight with stewards and police.
There was more controversy to come when Kris Commons grabbed Celtic's third in the 77th minute, moments after he was booked for simulation.
The Hoops midfielder was sent off for leaving the field of play in celebration as the visitors finished the game one point behind Old Firm rivals Rangers going in to the last game of the season on Sunday.
The spotlight will in time turn to Motherwell's visit to Parkhead and Rangers' game against Kilmarnock at Rugby Park but for the next few days the Lennon incident will dominate with investigations sure to to be carried out.
It was relatively calm beforehand.
As expected skipper Marius Zaliukas and keeper Marian Kello were restored to the Hearts team having been unavailable for selection in recent weeks, Kello due to a private matter and Zaliukas reportedly prevented from playing by majority shareholder Vladimir Romanov.
Eggert Jonsson kept his place after the Gorgie club appealed his sending off against Rangers at the weekend which added a little more intrigue.
Ironically, Lennon had vowed to keep his cool at a venue where, last November, he had been sent to the stand by referee Thomson after clashing with fourth official Steven McLean during a 2-0 defeat, and then charged with excessive misconduct by the Scottish Football Association.
However, despite having their third-place finish confirmed with Rangers' 2-0 win over fourth-placed Dundee United at Ibrox on Tuesday night, the Gorgie club had their own concerns, not least surrounding their recent form which had left them with only one win in their previous 10 games.
Yesterday manager Jim Jefferies was forced to insist he had no intention of resigning despite the interference of Vladimir Romanov in team selection.
It was against this backdrop an enthralling game began and the Parkhead side looked more at ease on the sodden pitch and zipped the ball around with some purpose and assurance.
In the 11th minute Commons made some space 25 yards from goal before sending a vicious shot wide of the target.
A minute later the Scotland midfielder was instrumental in Celtic taking the lead through Hooper.
He dispossessed a sluggish-looking Zaliukas to leave the Jambos defence totally exposed before setting up the former Scunthorpe striker with the easy task of slotting past Kello from inside the box.
The Tynecastle side looked in some disarray and moments later Hoops stopper Daniel Majstorovic headed a Commons corner from the left high and wide.
In the 25th minute, after Jambos midfielder Ian Black was booked for a two-footed tackle on Georgios Samaras - back in the side after suspension - Commons came close again.
Another powerful drive from outside the box saw Kello push the ball on to the post and when Celtic defender Mark Wilson cut the ball back it was cleared wide of the post, fortuitously for the struggling Jambos.
There was more trouble for Hearts in the 32nd minute when midfielder Obua was shown a straight red card by referee Thomson, after consulting with his linesman, after raising a hand to Mulgrew.
Television pictures suggested the dismissal was harsh and Hearts, fuelled by a sense of injustice, battled back in some defiance to get back in to the game but could not work Hoops keeper Fraser Forster.
Two minutes into the second half Forster had something to deal with and he clutched Rudi Skacel's low, whipped-in free-kick.
But in the 49th minute Hooper grabbed his second goal when he was set up by Ki Sung-yueng, the Celtic striker poking the ball past Kello from 12 yards.
Before the restart there was the astonishing incident when the fan came over the barrier and tried to attack Lennon.
Mayhem broke out as police and stewards intervened and when the ugly tussle ended the intruder was taken away up the tunnel by police.
Moments later, as the atmosphere became increasingly ugly, trouble broke out in the Celtic section of the stadium between supporters and police.
Meanwhile, on the pitch Kello had to make a great save from Commons to prevent Celtic stretching their lead further.
The game was almost rendered irrelevant as a poisonous atmosphere enveloped Tynecastle.
There was no way back for the Gorgie men and in the 77th minute Commons grabbed the third with a low drive from around 12 yards.
To add to the night of controversy, the Celtic midfielder was promptly sent packing by Thomson who awarded him another yellow for leaving the field in celebration.
The game petered out but the fall-out will go on for days, if not weeks and months.