Rangers have won eight and drawn one of their last nine games in all competitions, but the only dropped points came in a 2-2 draw at Dundee last weekend.
Kelsy had been dropped for that match and the Venezuelan international made his mark on his return to the side.
Ryan Naderi teed up his strike partner to open the scoring on 29 minutes.
Naderi and Kelsy added further goals in the second half before St. Johnstone were reduced to 10 men when Kai Fotheringham was shown a straight red card for a high challenge on Nico Raskin.
Substitute Tochi Chukwuani added a fourth with three minutes remaining to up the pressure on Celtic ahead of their trip to Hibernian on Sunday.
Elsewhere, Dundee United climbed into fourth thanks to Zac Sapsford's winner in a 3-2 victory over Aberdeen.
Falkirk beat Kilmarnock 3-0 to pull clear of the relegation battle, while St. Mirren snapped their losing streak with a 2-1 victory over Dundee.