Terrier benefited from three assists by Lovro Majer to inspire Rennes to a resounding victory with Lesley Ugochukwu also scoring to add to Yann Macon's own goal.
Rennes have 31 points from 17 games and trail leaders Paris St Germain by 11 points after the capital side salvaged a last-gasp 1-1 draw at RC Lens on Saturday.
St Etienne have 12 points.
Les Verts pressed high early on but it was a risky strategy and Rennes went 2-0 up in the space of five minutes.
Terrier was played through by Majer and beat Etienne Green from close range in the 23rd before doubling the tally with a clever back heel from another Majer pass.
On the stroke of halftime, Macon deflected Lorenz Assignon's strike into his own net.
Terrier completed his hat trick three minutes into the second half with a fine 20-metre shot into the top corner of the net after being set up by Majer.
Ugochukwu wrapped it up with a low cross shot seven minutes from time.