An Anthony Stokes double and strikes from Liam Henderson, Stefan Johansen and Kris Commons gave the Hoops a comfortable derby triumph as they wrapped up their third successive title in style.
It was to prove a disappointing night for the Jags, who had some good play in spells but were outclassed overall by the champions as Neil Lennon's side hit the goal trail.
After their recent good run of form came to an end against Inverness at the weekend, Thistle went into the Firhill clash determined to spoil the Celtic party and give their hopes of Premiership survival a huge boost after relegation rivals St Mirren lost to St Johnstone on Tuesday night.
But the Jags shot themselves in the foot with barely two minutes on the clock as Stokes rose well at the back post to put Lennon's side ahead.
And they were slow out of the traps after the break as well, Henderson left unmarked to net his first goal for the club and Johansen bursting into the box and coolly slotting home to all but kill off any hopes of a Thistle rescue act.
The Jags did pull one back late on when sub Christie Elliot finished well but things quickly turned sour for Archibald's side as they conceded twice more to suffer a heavy home loss.
The Jags boss said: "You could tell that they were on a mission from the off. They started really positively and, right from the start, they went after us.
"They got the early goal and it took the wind out our sails. We didn't get going until 20 minutes into the half when we had a wee bit of play.
"But we started the second half the same, we did the same thing again and, after that, it is hard to play a team in that form.
"The boys were well warned. We told them (to expect Celtic to start well). We knew with the crowd and everything that surrounded the game that that was going to be the case."
Next up for Archibald's side is a trip to St Johnstone on Saturday before they play their final pre-split fixture at home to Hearts on April 5 as the battle to beat the drop gets set to go down to the wire.
Thistle are two points ahead of the Buddies and one behind County and Kilmarnock in a four-way fight for survival and Archibald is determined to bounce back at the first opportunity.
He said: "We need to put that result behind us as quickly as possible. We have got another massive game on Saturday.
"We have not got much time. We spoke to the lads and we will chat about it today but our main focus is Saturday.
"We have got seven games now and it is seven cup finals for us."