The hosts managed to create a number of good opportunities throughout the game, but struggled to break down the visitors with Zlatan Ibrahimovic, Edinson Cavani and Ezequiel Lavezzi all wasting good opportunities.
Guingamp thought that they may have done enough to secure a point as the game entered stoppage time, before Thiago Motta’s teasing free-kick was met by the head of Alex, whose header forced a parried save from Mamadou Samassa, with Adrien Rabiot pouncing on the rebound to net from close range.
The win was assured moments later, when Ibrahimovic latched on to Gregory van der Wiel's long ball before bursting into the box to round the keep and slot into an empty net.
The champions moved to within a point of leaders Marseille, who host fellow title rivals Monaco on Sunday.
Lyon were consigned to playing UEFA Europa League football with a 4-0 aggregate loss to Real Sociedad in their midweek UEFA Champions League play-off and rounded off a difficult week with a surprise 2-1 defeat away to Evian.
A first-half brace from Kevin Berigaud was enough to give the home side the win, despite Lyon replying early after the break through Jordan Ferri.
Christian Romaric struck in the second half to secure a 2-1 win for 10-man Bastia at home to Toulouse.
Claudiu Keseru gave the hosts the lead two minutes before the break, after Julian Palmieri had been shown a straight red card for a high foot.
The visitors were level through Martin Braithwaite 13 minutes into the second half, but Bastia secured the victory when Romaric rose to head home a whipped Florian Raspentino cross nine minutes from time.
The result leaves Toulouse at the bottom of the table in Ligue 1, level on points with Sochaux, who were held to a goalless draw at home to AC Ajaccio.
Vincent Aboubakar scored the only goal of the game for Lorient as they edged past Valenciennes, who ended the game with 10 men when Rudy Mater was given his marching orders for a second bookable offence with five minutes to go.
In the day’s other games. Lille earned a point in a goalless draw at Rennes, while there were also no goals in the match between Reims and Nantes.
