Richards scored on a tough-angle shot 2:02 into the period as the Flyers overcame a pair of comebacks by the Blue Jackets.
Peter Forsberg and Freddy Meyer added goals for the Flyers, who snapped a club-record six-game home losing streak and stopped a three-game overall skid. Antero Niittymaki finished with 39 saves.
Jason Chimera and Rick Nash scored for the Blue Jackets, whose struggles continued, even with Hitchcock at the helm. Pascal Leclaire stopped 19 shots for Columbus, which tied a franchise record by losing its eighth straight.
The game was a matchup of teams with five wins each, the fewest in the NHL, and the play, at least early on, reflected that stat.
But this game was all about Hitchcock's return.
The 54-year-old coach struck a familiar pose, with arms folded, behind the bench for Columbus less than 48 hours after being hired. He replaced interim coach Gary Agnew, an assistant who took over after Gerard Gallant was fired on Nov. 14.
Just a month ago, Hitchcock was let go by Philadelphia after the Flyers opened the season 1-6-1 - the worst start in franchise history. He was fired on Oct. 22 and replaced by John Stevens, who was given a two-year contract on Monday.
The Blue Jackets had just one practice under Hitchcock before facing the Flyers, but put up a spirited effort, rallying from a pair of one-goal deficits in the second period.
In the end, it was Richards, scoring on a shot from the right circle - his first goal since March 11 - who made the difference.