A six-minute blitz early in the second half saw Saint Etienne defeat Lille 2-0 on Friday to strengthen their hold on fourth spot in Ligue 1 and move within a win of the northerners in third.
Brandao gave the hosts the lead in the 55th minute when he was allowed to ghost in at the back post to head the ball home before Franck Tabanou took advantage of more sloppy defending from Lille six minutes later to make it 2-0.
Having watched Cannes dump his side from the Coupe de France on Tuesday, Saint Etienne coach Galtier was relieved to see them respond at the Stade Geoffroy-Guichard.
"In the second half, opening the scoring, we had a huge advantage," the 47-year-old said.
"Tonight, the team that wanted the most, won.
"This is a beautiful performance... their courage, we were able to force things. My players were rewarded for their efforts.
"We have reduced the gap with Lille but the road is still long. Everyone should keep a cool head. I will be the guarantor of that mindset."
Saint Etienne moved to 37 points with their 11th win of the season, while Lille (40 points) completed their third league fixture without a win and could finish the weekend 10 points off top spot if Paris Saint-Germain defeat Nantes on Sunday.
Lille coach Rene Girard bemoaned his team's lack of focus early in the second half but refused to excuse his players for fatigue after playing three games in the space of 13 days.
"We played an hour during which we put this team, Etienne, (through) difficulties," Girard said.
"We then turned off after conceding the first goal.
"We will now try to solve it together with the players. I did not sense any physical problems."
Girard also conceded he was frustrated to see Florent Balmont sent off as the Lille midfielder protested what he saw as a foul by Tabanou on Djibril Sidibe in the lead-up to Saint Etienne's second goal.
"The red card received by Florent Balmont? He protested a little harder after the second goal where a foul has been committed on Djibril," the 59-year-old coach said.
"Whatever the outcome, it is still annoying to lose a player like him framework during a match."
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