Laquait deflected a Romain Hamouma header into his own net in the 77th minute as Les Verts, who occupy the Champions League qualifying spot, leapfrogged Lyon on goal difference with seven matches remaining.
Lyon slumped to a 1-0 defeat at Stade Reims as they lost for the third straight time in Ligue 1, finishing the game with 10 men following Milan Bisevac's red card early in the second half.
Saint-Etienne, who are unbeaten in 16 games in all competitions in 2013, dominated possession throughout but increased the pressure until Laquait was forced into his costly mistake after Hamouma's header from a Francois Clerc cross.
Saint-Etienne have 53 points with a goal difference of +26 compared to Lyon's +16 and the two teams are four points behind Olympique Marseille.
"We won because we never gave up," St Etienne coach Christophe Galtier told a news conference.
"But if we wanted to win we first needed not to concede any goal and we defended well. The most important thing was to keep our rivals at bay."
Evian have a tough task on their hands as they dropped to 17th on 31 points only one point above safety.
Reims are 15th on 34 points after Grzegorz Krychowiak scored from the penalty spot in the 53rd minute after Bisevac was sent off for a foul in the box on Diego Rigonato.
Lyon were dominated in the first half and Benoit Vercoutre parried away Christopher Glombart's powerful shot from just inside the box in the 12th minute.
He then pulled off a brilliant save to deny Gaetan Courtet's volley on the half hour as Lyon looked incredibly shaky at the back.
Kossi Agassa tipped Clement Grenier's free-kick over the bar as the visitors searched for an equaliser in the second half but it was as close as they got.
On Saturday, Paris Saint-Germain restored a seven-point lead at the top over second-placed Marseille with a 2-0 win at Stade Rennes after their title rivals beat Girondins Bordeaux on Friday.
Later on Sunday Lille moved up to fifth on 52 points with a crushing 5-0 defeat win over Lorient as they continued their bid for a European place.
Salomon Kalou opened the scoring with a low crossed shot in the second minute and Dimitri Payet doubled the tally six minutes later, tapping in after Fabien Audard had parried a Ronny Rodelin shot into his path.
Lucas Digne made it three from the penalty spot after half an hour with Kalou adding a fourth shortly after from close range when Payet's strike bounced off the post into his path.
Rodelin headed home Lille's fifth early in the second half for the rampant hosts.
