Souquet hit an unstoppable shot beyond Anthony Lopes three minutes before half-time and Lyon's hopes of mounting a response were hit six minutes into the second half when Youssouf Kone collected a red card for headbutting Andy Delort off the ball.
Montpellier had much the better of the first half but could only carve out a series of half-chances in the opening half an hour.
They were awarded a penalty in the 35th minute when Joachim Andersen pulled down Delort in the area, with the Lyon defender earning a yellow card for his protests.
Delort missed from the spot, his shot striking the outside of the right post, but it would not matter as Montpellier took the lead five minutes later.
Lyon could only half-clear a corner and it was returned with considerable interest as Souquet caught it on the half-volley, the ball flying beyond the motionless Lopes.
After Youssouf clashed with Delort to collect red early the second half, Lyon had to rely on set-pieces, but the closest they came to an equaliser was a Jason Denayer header which brushed the outside of the post on the hour.