The Grecians started brightly, but rarely looked like recovering after falling behind to Steve Jones' 29th-minute opener, with the Saddlers wide man doubling his tally in first-half stoppage time.
Richard Duffy's dismissal for a second yellow card killed off any lingering hopes of an Exeter comeback before Troy Deeney added a third with a fine run and shot in the 70th minute.
Hutchings said: "In the first 25 minutes we were not at the races and did not come to terms with the way they were playing.
"But obviously we scored two very good goals in the first half even though it was against the run of play to be honest."
A relieved Hutchings added: "We dominated in the first part of the game at MK Dons last week and came away with nothing. So it's swings and roundabouts."