Woll made 18 saves in the second.
"It's been a little crazy. I found out [I was starting] today around 1 p.m. that I was going to be able to play," Woll said. "It was pretty special to come out here and get the win tonight. It was playoff-style hockey. Our guys were out diving and blocking shots."
O'Reilly extended the Maple Leafs lead to 4-2 at 12:33 of the third period on a rebound after a shot by Matthew Knies.
Knies, who played for the University of Minnesota in the NCAA Frozen Four here last week, had an assist for his first NHL point.
"It's intense out there, it's fun to be a part of," Knies said. "Everyone has been so welcoming the past few days, it was easy to jump in and try to make an impact."
Sergachev scored at 13:49 with a one-timer from the high slot for the 4-3 final.
"It was a weird game with way too many penalties for both teams," Lightning captain Steven Stamkos said. "Probably not how it's going to be during playoff time, but still, I think we have some areas we need to improve."
NOTES:The Lightning held a pregame ceremony for Stamkos to celebrate his 1,000th NHL game, which he played last Thursday against the New York Islanders. ... Woll had the most saves by a Maple Leafs rookie goalie since Peter Ing made 46 against the Chicago Blackhawks on Oct. 18, 1990. ... With Samsonov scratched, Matt Onuska served as Toronto's backup goalie. Onuska plays for Windsor of the Ontario Hockey League. … Sergachev has seven points (two goals, five assists) in the past six games.