Chris Stewart had a first-period goal for the Blues, outscored 23-9 during an 0-4-1 slump. Perron beat Sergei Bobrovsky from the slot for his sixth goal at 9:51, also the Blues' first shot of the period.
Jaroslav Halak made 18 saves, giving up his first goal at home in 168 minutes, 32 seconds on Matt Calvert's short-handed tally late in the second, a streak that dated to March 31, 2012.
Bobrovsky made 21 saves for Columbus, last in the NHL with 12 points. The Blue Jackets are 1-4 on a six-game road trip that ends Sunday in Chicago. New team president John Davidson, the Blues' president the previous seven seasons, made the trip.
Halak is 16-1-1 in his last 18 home starts during the regular season, with the lone loss coming against Columbus 5-2 on March 31, 2012. The Blues are 13-2-1 in their last 16 at home against the Blue Jackets.
The standing-room attendance of 19,457 was the Blues' second sellout of the season.
The Blues' Barret Jackman broke a franchise durability record for a defenseman, playing in his 616th game. St. Louis' first-round pick in 1999 vaulted from fourth to first in rapid fashion, overtaking Bob Plager (615), brother Barclay Plager (614) and Al MacInnis (613). Teammates stood on the bench beside him when the record was announced during a break in the first period.
David Backes set up the go-ahead goal when he carried the puck over the blue line and then skirted a check against the boards before passing to Perron.
The Blue Jackets were carrying play early with a 10-5 advantage in shots before Stewart scored his seventh on a high drive from just above the right circle at 13:55.
Columbus was outshot 13-3 in the second but tied it late with its second short-handed goal of the season. Calvert capitalized on a giveaway by Matt D'Agostini for his third of the season despite losing control of the puck in tight against Halak. An assist went to James Wisniewski, who hit the crossbar a few minutes earlier and slammed his stick on the boards in frustration.
Bobrovsky had a strong game in net for Columbus, unlike Jan. 31 at home when he was pulled after giving up three goals on 11 shots in a 4-1 loss.
NOTES: The home slump was the Blues' worst since an 0-6-1 tailspin Nov. 25 to Dec. 17, 2006. ... Columbus F Derek Dorsett was driven into the boards helmet-first by a check from Roman Polak in the second period but didn't miss a shift. Dorsett had stopped and turned his body to control the puck with his skate before the hit. ... Columbus C Artem Anisimov, taken off the ice on a stretcher Thursday night after getting struck in the head at Detroit, was among the scratches.