Zherdev missed all of pre-season camp and the club's first two games, arriving in Columbus on Sunday from his native Russia after ironing out visa problems.
He scored on the power play just 1:01 in and added another when he jammed in Rick Nash's shot midway through the second period to make it 3-1.
Nash and Duvie Westcott each added a goal and two assists, Anson Carter scored his first with Columbus, and David Vyborny had three assists for the Blue Jackets, who had three power-play goals for the second game in a row.
Nash, Westcott and Vyborny have points in all three Columbus games.
Ed Jovanovski scored for the Coyotes, who have lost two in a row after a 6-3 win over the New York Islanders in the season opener.
Zherdev was involved in a protracted and contentious contract dispute with Columbus general manager Doug MacLean throughout the summer. He finally signed a US$7.5 million, three-year deal on Sept. 28.
With the score tied at 1-1 midway through the second period, the Blue Jackets pulled away. Nash was camped in front of the net during a power play and chipped Vyborny's pass from the right wing into the high left corner of the net for his third goal.
In the midst of six consecutive power plays - Columbus was 3-of-12 with a man advantage - the Blue Jackets made it 3-1 when Nash carried the puck along the left boards, shed defender Derek Morris and muscled his way to the net. He got off a shot at the near post, with Zherdev trailing to jam the puck in.
Carter, a free agent signed as insurance in case Zherdev didn't ink a contract, scored 1:27 into the third period. He took a pass, steadied the puck with his skate, and backhanded it toward the net, where the shot caromed off Jovanovski's left skate and past Phoenix goaltender Michael Morrison.
Just 61 seconds in, Nash swooped in on Morrison, who blocked the shot. But Zherdev cleaned up for a goal on his first shot of the season.
Jovanovski, signed in the off-season away from Vancouver, tied it midway through the first period. Shane Doan skated along the back boards and curled alongside the right circle before sliding a cross-ice saucer pass that Jovanovski netted from the right hash.
Notes: Columbus C Dan Fritsche injured a shoulder in the first period and didn't return. ... Phoenix D Keith Ballard hurt his hand in the opening period. ... The Blue Jackets have only won two games in a row in October twice before in their five-year history. ... Morrison, Curtis Joseph's backup, got the start for Phoenix after telling Coyotes coach Wayne Gretzky he had friends and family in Ohio.