Frank Lampard's side went into the match without a win in any of their three previous Premier League games, a run that had seen their coach come under increased pressure. Although they were able to end that streak, the performance was by no means vintage.
Chelsea had the better of the first half but did not begin to exert genuine control until after Antonee Robinson's dismissal in the 44th minute left the Blues with a numerical advantage.
They had great difficulty making the most of that sending off, but eventually Mount struck 12 minutes from time to move Chelsea back up to seventh in the table.
Chelsea briefly appeared to find their groove when they created a flurry of chances in quick succession before the half-hour mark of the contest.
Alphonse Areola had to be alert twice, saving from Olivier Giroud and Antonio Rudiger either side of Mount striking the crossbar during what was a promising three-minute spell from the visitors.
While that was not the start of a prolonged onslaught, Chelsea's chances were helped just before half-time when Robinson was shown a straight red for a wild tackle on Cesar Azpilicueta that completely missed the ball and sent the Spaniard flying.
Despite having an extra man, Chelsea's chance creation frequency did not appear to increase, two of their better opportunities ultimately resulting in offside calls.
A defensive calamity just past the hour then almost saw Chelsea fall behind, as Azpilicueta's poor pass forced Edouard Mendy to stretch and nudge the ball to Ivan Cavaleiro, but luckily Thiago Silva was in attendance to block his shot in front of an empty goal.
Chelsea finally found a way through in the latter stages, Mount drilling a volley low past Areola after the Frenchman had diverted a left-wing cross right to him.
