Toews cut it to 3-1 at 6:02 of the second, but Nick Schmaltz scored for Arizona to make it 4-1 at 8:25.
"First time playing the old team, and you get two wins in five days, that's exciting," said Schmaltz, who was traded by Chicago for Strome and Brendan Perlini on Nov. 25, 2018. "I was excited both games and I felt like I had a little extra something."
Strome scored a power-play goal at 12:58 of the third to get Chicago within 4-2.
Keller scored his second of the game at 17:53 for the 5-2 final.
He had 12 shots on goal, tying three others for the Coyotes/Winnipeg Jets record. Arizona has had at least 40 shots on goal in three consecutive games, the fifth such stretch in Coyotes/Jets history and first since March 5-9, 1996.
"We've giving up really easy chances and we're having to work hard for ours, and it's not a good combination," Lehner said. "We're giving up way too much, and it's a hard climate to defend in right now for everyone."