A second-half hat trick from Olivier 1 win at Sochaux on Saturday, moving the club to the top of the Ligue 1 table.
Giroud netted his first goal in the 50th minute to put his team in front, but after Sochaux's Abdoul Camara equalized six minutes from time, Giroud tallied two more goals in the final minutes to secure a fifth win in six games for his side.
Montpellier moves three points clear of second-place PSG with the win, while Sochaux remains in the middle of the table having lost its last two games.
Sochaux nearly took the lead in the first half when Edouard Butin's volley smashed against the crossbar, but five minutes into the second half, a poor clearance allowed Giroud to stab the ball home from close range.
The hosts were level six minutes from time as Camara finished off a free kick from Marvin Martin, only for Giroud to score on the counter-attack with a nice chip a few minutes later.
The hat trick was then completed in the final minutes when Younes Belhanda picked out Giroud in space and he fired past goalkeeper Teddy Richert.
Lille 2, Brest 0
Lille, France - Lille extended its unbeaten streak in Ligue 1 to 13 games on Saturday after securing a 2-0 win at home over Brest.
The home side entered the match having drawn its last three games, but Dimitri Payet got the team off to a strong start as he combined with Tulio De Melo to put Lille ahead after 11 minutes.
Eden Hazard had a shot come back off the crossbar midway through the first half as Lille pressed to extend its lead, but the win was safe a few minutes from time as Moussa Sow finished off a cross from Hazard to wrap up all three points.
Dijon 2, Nancy 1
Nancy, France - Dijon won its second game in a row on Saturday as a goal from Younousse Sankhare in the 83rd minute secured a 2-1 victory at Nancy.
Dijon's successive wins come on the back of a four-game losing streak, moving the club three points clear of the drop zone and snapping a two-game winning streak for Nancy.
The two sides traded goals in the first as Dijon took the lead through a successful penalty kick from Eric Bautheac, only for Djamel Bakar to answer eight minutes later for Nancy.
But Sankhare struck the decisive blow with seven minutes to play when he headed home Thomas Guerbert's corner kick.
Bordeaux 2, Caen 0
Bordeaux, France - Bordeaux moved out of the relegation zone on Saturday as the club got second-half goals from Yoan Gouffran and Anthony Modeste in a 2-0 win over Caen.
The victory is the first at home this season for Bordeaux and is just the second in the last 11 games for the team.
It took nearly 60 minutes for the opening goal to arrive and it came when Nicolas Maurice-Belay played a pass to Gouffran at the edge of the penalty area. He then settled the ball and fired it past goalkeeper Alexis Thebaux to put the hosts in front.
Modeste entered the match as a substitute in the 67th minute and he put the result away 11 minutes from time by taking advantage of a turnover by Caen defender Molla Wague to beat Thebaux.
St Etienne 3, Ajaccio 1
Saint Etienne, France - St Etienne won for the fourth time in six games on Saturday by claiming a 3-1 win over last-place Ajaccio.
A seventh-minute strike from Max-Alain Gradel was followed by a goal from Florent Sinama-Pongolle before the break.
Fousseni Diawara pulled a goal back on the hour mark for Ajaccio, but Banel Nicolita's second goal of the campaign six minutes from time ensured Ajaccio of a fifth loss in six games.
Rennes 3, Evian 2
Rennes, France - Rennes kept pace with Montpellier near the top of Ligue 1 on Saturday as Julien Feret's 87th-minute penalty kick gave the home side a 3-2 win over Evian.
The visitors took a 2-1 lead into halftime with goals from Cedric Barbosa and Daniel Wass, but Youssouf Hadji equalized for Rennes in the 77th minute and Evian's Olivier Sorlin was called for handling the ball inside his own penalty area, giving the Feret the chance to win the match from the spot.
Evian entered the match on a four-game winning streak, but remains two points above the drop zone with the loss.
Toulouse 2, Valenciennes 0
Toulouse, France - Toulouse maintained a place in the top five on Saturday by notching a 2-0 win at home against Valenciennes.
After scoring just one goal in its past six games, Toulouse took the lead in the 25th minute through Paulo Machado, while Antoine Devaux added another goal midway through the second half.
Valenciennes managed few chances over the course of the match and the hosts almost made it 3-0 in the final minutes when a shot from Emmanuel Riviere was cleared off the goal line.