Neil Lennon's side had appeared to be heading for a another win after coming from behind to lead 3-1 against St Johnstone late on at McDiarmid Park.
Goals from Kris Commons, Teemu Pukki and Virgil van Dijk had given the Scottish champions a comfortable two- goal lead in Perth last night.
But they switched off in the final 10 minutes to gift goals to Scott Brown and Michael O'Halloran and somehow snatch a draw from the jaws of victory.
The Parkhead club will be unable to break through the century mark for points even if they beat Dundee United in their final game at home this Sunday.
Lennon had made no fewer than six changes to the starting line-up which had thrashed second-placed Aberdeen 5-2 at Parkhead on Saturday.
Lukasz Zaluska was given a rare outing between the sticks - he had not featured since the League Cup defeat to Morton back in September - as Fraser Forster was rested.
In defence, Mikael Lustig came in on the right with Adam Matthews ahead of him. Meanwhile, Beram Kayal and Derk Boerrigter were handed run-outs in midfield.
And up front the rarely-seen partnership of Amido Balde and Pukki started as Leigh Griffiths and Anthony Stokes both dropped to the bench.
The home team started the game brightly and struck the woodwork within just 30 seconds of the game getting underway.
O'Halloran unleashed a shot from fully 25 yards out and his ambitious attempt hit the right post. Polish stopper Zaluska could, given his lack of first-team involvement, be forgiven for being somewhat rusty, but he looked sharper when called into action in the eighth minute.
Lee Croft picked out Stevie May in the visitors' box and the newly-crowned Scottish Football Writers Young Player of the Year got a shot on target from an acute angle. The keeper, though, blocked it.
However, Tommy Wright's side took the lead shortly after that from a Croft corner.
Steve Anderson angled a downward header at goal and Tim Clancy prodded it into the roof of the net. Celtic could offer little in the way of a response to that.
Balde worked hard for an opening and Pukki tried his luck from long range. But neither frontman could level the tie.
St Johnstone should have edged further in front in the 42nd minute when they were awarded a penalty by referee Steven McLean after Kayal brought down O'Halloran.
May, looking for his 28th goal of the season and his first against Celtic, stepped forward to take the spot kick, but his shot was saved by Zaluska.
The Saints striker went to ground clutching his right knee after being involved in an accidental collision with Efe Ambrose shortly before half-time.
There was a collective gasp from the St Johnstone fans inside McDiarmid Park as their hopes of landing the William Hill Scottish Cup rest heavily on the scorer's fitness.
He appeared to be fine after receiving treatment from the Perth club's medical staff, but did not reappear for the second half. His place was taken by Nigel Hasselbaink.
Lennon, too, made two changes in an attempt to lift his side's performance.
He needed to as the showing in the first 45 minutes had fallen well short of the standards expected. He removed Boerrigter and Matthews - both of whom had been virtually anonymous - and replaced them with Commons and club captain Scott Brown.
That pair linked up to devastating affect to help Celtic level in the 53rd minute. Brown played a neat one-two with Commons and was tripped by Gary McDonald.
Commons stepped forward to take the penalty and powered his shot straight down the middle as Alan Mannus dived to his left to claim his 31st goal of the 2013/14 campaign.
Finnish striker Pukki justified his start in the 73rd minute when he side-footed a square ball from Mulgrew beyond the clutches of Mannus and into the net.
Van Dijk looked to have put the result beyond doubt four minutes after that when the ball broke to him on the edge of the St Johnstone penalty box and he volleyed into the bottom left corner.
Wright threw on former Scotland striker Chris Iwelumo for Croft in the hope the giant forward could haul his side back into the game.
Iwelumo did not net himself, but his side scored twice in as many minutes to snatch an unlikely draw.
Saints midfielder Brown scored a deflected goal in the 84th minute and then O'Halloran netted a diving header a minute later.
Despite sewing up the title some time ago, it was a painful climax to an entertaining match for Celtic and will not go unnoticed by manager Lennon as he lays his plans for next season.