Mackay-Steven and Armstrong arrived from Dundee United on transfer deadline day and both wasted little time in making their mark at Firhill.
It look winger Mackay-Steven less than a minute to open his account for Celtic, receiving the ball inside the penalty area from a corner and firing low past Partick goalkeeper Scott Fox.
Armstrong then put the visitors in a commanding position on the half-hour mark, having been played in by John Guidetti.
Partick pushed forward in search of a goal in the second half and they were denied a penalty after strong claims for handball against Emilio Izaguirre in the area.
But Celtic sealed the points in the 66th minute when Stefan Johansen fire a shot inside the far post, ensuring Ronny Deila's men opened a three-point lead over rivals Aberdeen.
