Jesse Puljujarvi made it 3-1 with a power-play goal at 9:14 of the third period. He dove for a loose puck in front off a face-off and chopped it in between the pads of Sorokin.
Smith won for the first time since Oct. 16, the second game of the season against the Flames. He missed 26 games with a lower-body injury, then returned to play three games before sustaining a thumb injury, missing another eight games.
"It was an emotional 24 hours, [Tippett] and Jimmy [Playfair] have been a big part of my career," Smith said. I owe a lot to 'Tip' and what he has done for me.
"From a personal standpoint, it's difficult, but it's part of the business and we have all been through it a time or two. For [Woodcroft] to come in and [Dave Manson] to come in on short notice on a game day, they were able to get their message across and we were humming right from the drop of the puck. It was nice to see, and to win is the important thing, so that was great too."
NOTES: Woodcroft is the fifth Oilers coach to win his NHL debut, joining Todd Nelson (Dec. 30, 2014), Ralph Krueger (Jan. 20, 2013), Craig MacTavish (Oct. 6, 2000) and George Burnett (Jan. 20, 1995). … Oilers defenseman Markus Niemelainen had two shots and a game-high seven hits in 11:00 after being called up from Bakersfield on Thursday to replace Duncan Keith, who is out 2-4 weeks with an upper-body injury. … Broberg, also recalled Thursday, was plus-1 in 11:38. … Hyman has scored 212 points (100 goals, 112 assists) in 384 NHL games in seven seasons with the Oilers and Toronto Maple Leafs.