John Still's side had not suffered defeat in league action since early September prior to their trip to the Pirelli Stadium, but Phil Edwards' 47th-minute looping header won it for the hosts.
Luton also had Luke Wilkinson sent off in stoppage time as they fell to third.
Gareth Ainsworth's side fell behind to an early Steve Elliott strike at Cheltenham Town, but the visitors were level within a minute through Paris Cowan-Hall.
Lee Vaughan's dismissal gave Wycombe a man advantage, and they went on to secure victory thanks to goals from Steven Craig, Joe Jacobson and substitute Matthew McClure as it ended 4-1.
Jamie Collins' first-half double appeared to have put Micky Mellon's side on course for a third successive away win in the league, but Exeter mounted a comeback after the break.
Nichols then secure the win in injury time with a looping header.
Bury suffered only their second home league loss of the season as Newport County won 3-1 at Gigg Lane, while managerless Mansfield Town reacted to Paul Cox's exit with a 1-0 win over Plymouth Argyle.
At the bottom , Hartlepool United were given early hope against York City when Scott Fenwick opened the scoring, but Russ Wilcox's side came surging back after the break to record a 3-1 win - centre-back Keith Lowe netting twice in as many minutes.
Carlisle United are just outside the bottom two after a 4-2 defeat against fellow strugglers Dagenham and Redbridge, while Oxford United were held to a goalless draw by AFC Wimbledon.
Meanwhile, Portsmouth claimed a 3-0 victory over Morecambe, Accrington Stanley beat Cambridge United 2-1 and Northampton Town edged Stevenage 1-0.
