That’s more like it.Sheldon Keefe’s debut game as head coach of the Maple Leafs couldn’t have gone any better as Toronto cruised to a much-needed 3-1 win over the Arizona Coyotes in Glendale, Ariz., Thursday night. All eyes were on Keefe’s lineup decisions as the Leafs headed into Thursday’s game mired in a six-game losing streak that cost previous coach Mike Babcock his job, and the players responded. Tyson Barrie, Pierre Engvall and Auston Matthews each scored goals as the free-flowing Leafs outshot the home team 32-31.MORE: What exactly is the Kyle Dubas-Sheldon Keefe connection?Perhaps most impressive was the way the Leafs protected the puck, allowing just four giveaways over the course of the game (the Coyotes had 13). Careless play while in possession was a hallmark of the Leafs’ struggles in recent weeks, so the team’s ability to hold onto the puck — while also successfully killing off all three penalties on the night — was a step in the right direction.Toronto improved to 10-10-4 on the season with the victory.Here are three takeaways from Thursday’s game.Keefe’s LeafsIt was apparent from the morning skate that the new bench boss would be changing things up a bit, as Keefe implemented several changes ahead of Thursday’s contest. At game time, there were some notable differences in the Leafs’ lineup from Mike Babcock’s final game in charge. Ilya Mikheyev joined the top line alongside John Tavares and Zach Hyman, Tyson Barrie started alongside Morgan Rielly on the blue line, Jason Spezza moved up to the third line, Pierre Engvall made his NHL debut and Nick Shore sat after playing in 18 straight games.Here’s how the Leafs line up tonight.Presented by @cocacola_ca. #LeafsForever pic.twitter.com/N47iQLh3F5— Toronto Maple Leafs (@MapleLeafs) November 22, 2019The players seemed to immediately respond to the new-look lineup, coming out of the gates with much more of a jump than had been seen in weeks. And with Barrie’s first-period opener, the team held an advantage on the scoreboard for the first time in nearly 450 minutes of action.This is the #Leafs first lead in 446:47 of action— Sportsnet Stats (@SNstats) November 22, 2019Barrie, the bomber?Speaking of Tyson Barrie, the defenseman’s goal was his first in a Toronto uniform, and it couldn’t have come any sooner.The 28-year-old’s struggles with the Babcock-led Maple Leafs have been well-documented, with Barrie telling the media earlier this month that his lack of offensive output had been weighing on him. While Barrie never placed his woes on Babcock, the former Colorado Avalanche standout’s time as an offensive catalyst diminished during the 23 games that the now-fired coach was in charge this season.With Keefe taking the reins, Barrie was immediately given more offensive responsibility, including a move to the top power play unit.His first Leaf goal came at even-strength, but it may not be a coincidence that Keefe’s vote of confidence in Barrie’s abilities allowed the beleaguered blueliner to get a goal in his first opportunity under the new boss.Familiarity breeds successWhile the coach was making his NHL debut on Thursday, Pierre Engvall was stepping into his second game in the big leagues.Engvall’s maiden contest was on Tuesday under Babcock, when he played 14 shifts for 9:27 of ice time but didn’t have much of an impact. It’s to be expected for a young, non-superstar player making his debut well into the season — you take what you can get and just hope to feel things out quickly.Babcock’s exit meant Engvall fortuitously skipped over the “getting to know you” phase with his coach as Keefe was already intimately familiar with what the 23-year-old could do thanks to their time together with the Marlies. That familiarity became apparent in the second period when Engvall was deployed on the penalty kill after William Nylander was sent to the box for high-sticking. Engvall’s speed in transition is something that Keefe had used strategically in the AHL, and his gamble to do so on the PK at the NHL level paid immediate dividends as the Swede collected the puck at the Leafs’ blue line and left the Coyotes players in his wake en route to his first-ever NHL tally — a shorthanded goal to boot.Engvall’s finish was worthy of the big leagues, but he might need to put in some work on his celebrations.