The pair joined Celtic from Dundee United in a combined £2m Deadline Day deal, and they had dream debuts.
Mackay-Steven scored with his first touch in a Celtic shirt just 38 seconds into the game, and Armstrong added the second on the half-hour mark.
Mackay-Stevens’ goal was not the fastest in the Scottish top-flight this season – Armstrong still has that record having scored 32 seconds into the Dundee derby earlier this season.
They are the first pair of debutants to score for the Hoops since 1987 when Andy Walker – in the Sky commentary box on Wednesday night – and Billy Stark got their Parkhead careers off to a flyer against Morton.
The victory means the reigning champions are three points clear of second-placed Aberdeen with a game in hand, and their eighth consecutive domestic win looked inevitable from the moment Mackay-Steven scored.
Partick failed to deal with Stefan Johansen’s corner, and when the ball ricocheted to Mackay-Steven, 10 yards out, he fired a low shot past Scott Fox.
Armstrong brought a save out of Fox three minutes later, and the Thistle keeper then did well to keep out a rising Johansen effort.
On the half-hour though, Celtic got the second with a superb team move. Mackay-Steven powered forward and fed Armstrong on the edge of the box. He shipped the ball on to John Guidetti, whose poor first touch took him away from goal, but he recovered well, turned on a sixpence and pulled the ball back for Armstrong to lash the ball past Fox.
Partick could create little, with Johansen and Scott Brown dominating the centre of the park, snapping at heels and breaking up the play.
The hosts were better in the second half, Ryan Stevenson and Lyle Taylor doing their best to haul their team back into the game.
Stevenson’s fine cross from the left wing almost found the willing Taylor, but Virgil van Dijk arrived just in time and put him off.
There was a shout for a Thistle penalty just after the hour mark when Stuart Bannigan’s powerful shot was blocked by Hoops left-back Emilio Izaguirre inside the box – it might have been an elbow – but referee Crawford Allan took no notice.
Johansen made sure of the points on 66. Nir Biton’s headed clearance down the middle found its way through to the Norwegian – outstanding all evening – and he advanced to the edge of the box and fired home a superb low shot with his left foot to wrap it up.
Partick huffed and puffed but never really threatened Craig Gordon, who kept his eighth consecutive clean sheet – he is now unbeaten in 710 minutes of football.
The Jags are down in ninth and have now won just one of their last nine games.