Kessel's 19 points (five goals, 14 assists) lead the Penguins, who are averaging 2.63 goals per game after finishing No. 1 in the NHL at 3.39 last season.
Pittsburgh (9-6-2), coming off a 1-3-1 road trip, scored more than two goals for the second time in its past nine games. Arizona (2-13-2) is 1-8-1 on the road.
After failing to score more than one even-strength goal in each of their past five games, the Penguins scored two in the first 3:07 of the first period to take a 2-0 lead.
Schultz opened the scoring by one-timing a pass from Malkin below the left face-off circle. The sharp-angled shot deflected off goalie Antti Raanta's right skate and into the net for Schultz's second goal of the season, first since Pittsburgh's season-opening 5-4 overtime loss to the St. Louis Blues on Oct. 4.
Schultz played 20:31 on 24 shifts after missing the previous six games with a concussion sustained Oct. 24 against the Edmonton Oilers.
Malkin batted in a rebound off a shot from Kessel to make it 2-0.
"[Scoring 5-on-5] certainly improves your chances of winning exponentially," Penguins coach Mike Sullivan said. "We've put probably four games together now where we've generated a significant amount of chances 5-on-5. So, even tonight, we had a lot of real high-quality chances that we didn't convert on.