Morgan Sanson, on as a substitute for Payet, guided home a header from a Kevin Strootman cross two minutes after the interval as Marseille won for the first time since late November.
Caen played most of the second half with 10 men after Frederic Guilbert was dismissed for a second booking.
Marseille had faced angry supporters in heated exchanges following last weekend’s 1-1 home draw with Monaco, the culmination of a dismal run that included a humiliating French Cup defeat by fourth-tier amateurs Andrezieux at the start of the month.
Rudi Garcia’s side climbed to seventh following Sunday’s victory and to within five points of the Champions League spots after inflicting a fifth home defeat in six outings on a Caen outfit with just three wins all season.
Kylian Mbappe and Edinson Cavani both scored hat-tricks on Saturday as Paris Saint-Germain romped to their biggest-ever home win with a 9-0 thrashing of bottom side Guingamp.
Meanwhile, Thierry Henry’s nightmare spell in charge of Monaco took another turn for the worse as Cesc Fabregas gifted Strasbourg a goal and fellow new signing Naldo was shown a seventh-minute red card in a 5-1 home humbling.