Ryan Malone, Maxime Talbot, Ryan Whitney, Jarkko Ruutu, and Ronald Petrovicky also scored, and Sergei Gonchar added a pair assists for the Penguins, who have won five of six.
Shane Doan and Steve Reinprecht scored for the Coyotes, who have lost five of eight since winning a season-best seven straight.
Crosby helped the Penguins take the lead for good midway through the second period. Crosby wound up to shoot the puck from the outside edge of the right faceoff circle but instead passed to Whitney, who one-timed the puck past Mikael Tellqvist from the bottom of the left circle to break a 2-2 tie.
Ruutu extended Pittsburgh's lead to 4-2 at 17:37 of the second when he slid the puck between Tellqvist's pads from the left circle.
Crosby added to his season's highlight reel at 4:48 of the third, scoring with a backhand flick from the right faceoff circle as he fell to the ice to make it 5-2.
Petrovicky scored 15 seconds later to give Pittsburgh a 6-2 lead, and Recchi added a power-play goal at 12:16 to cap the scoring with Crosby earning his third assist.
Crosby needed only 24 seconds to make his presence felt in his first visit to Phoenix. Standing behind the net, Crosby left his skates to lunge forward and pass the puck to Malone in front of the crease for the goal and a 1-0 lead.
Doan tied the score 1-1 at 11:36 of the first, taking a pass through the crease from Ladislav Nagy and beating Jocelyn Thibault with Phoenix on a 5-on-3 power-play.
Talbot put the Penguins ahead 2-1 on a blast from the point at 13:32 of the first. Reinprecht tied the score 2-2 at 10:37 of the second period on a wrist shot off a scrum in front of the net.
Notes: Recchi has six goals in his last three games and 13 points (seven goals, six assists) during his current six-game points streak. ... Crosby also has a six-game points streak, with four goals and nine assists in that stretch. ... Crosby and the Penguins did what even the Detroit Red Wings couldn't do this season - sell out Jobing.com Arena. A standing-room crowd of 18,495 was on hand to see Crosby's lone visit to the Valley during the current three-year scheduling cycle. ... Pittsburgh and Phoenix were playing for the first time since February 25, 2004, when the Penguins won 4-3 in overtime. ... Doan moved within one goal of Doug Smail for fifth place on the Coyotes' career list with 188. He has 10 goals and nine assists in his last 15 games.