Lions striker Neil Harris spurned a chance to claim a point when he failed to beat Wycombe goalkeeper Tom Heaton with a second-half penalty.
The early pressure came from the visitors, and Chris Hackett's powerful strike from the edge of the box after 20 minutes forced a good save from on-loan goalkeeper Heaton.
On the stroke of half-time the hosts snatched the lead when Kelly curled a cross in from the right which eluded everybody and found its way into the far corner.
Millwall put the home side under pressure for large parts of the second half and appeared to get their reward when Shaun Batt went over in the box, but Heaton saved the penalty superbly.
Gareth Ainsworth's elbow on Tony Craig saw him sent off late on and Kenny Jackett's men pushed forward in the last 10 minutes, but the Chairboys defence held out.