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. 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 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.
The Flyers opened the scoring midway through the first period, when Forsberg scored his seventh of the season on a power play. The Flyers captain, who sat out Wednesday night's loss to Ottawa because of a sore back, deflected a wrist shot from the point by Lars Jonsson at 9:59. The goal marked the 11th straight game that Columbus trailed 1-0.
The Blue Jackets had a two-man advantage for 1:34 when Kyle Calder and Derian Hatcher were whistled for hooking, but managed few real scoring chances on Niittymaki.
They carried the bulk of the play in the second period and outshot the Flyers 19-7.
Columbus tied it at 12:31 of the second as Chimera backhanded a rebound past Niittymaki for his third of the season.
But Meyer put the Flyers ahead with less than two minutes remaining in the period, taking a pass from Mike Knuble while storming in from the right point and one-timing a shot past Leclaire for his second.
Columbus then capitalized on Joni Pitkanen's hooking penalty.
Nash positioned himself just to the left of the net. After a shot by Sergei Fedorov caromed off the back boards, Nash grabbed the puck and sent it into the open net with Niittymaki out of position, making it 2-2 with 18.9 seconds left.
Notes: Hitchcock is 408-250-100 in 758 regular-season NHL games. In 503 games as coach of the Dallas Stars from 1996-02, he went 277-166-60-7. He won the Stanley Cup with the Stars in 1999. ... The Blue Jackets sent LW Alexandre Picard to AHL Syracuse. ... Philadelphia is 5-8-2 since Hitchcock was fired.