McDonagh set up Mathieu Joseph's goal at 17:56 that gave Tampa Bay a 2-1 lead.
Nick Foligno tied it 2-2 for Columbus with a deflection on the power play at 47 seconds of the third period.
Blue Jackets first-line center Pierre-Luc Dubois played an NHL career-low 3:55 with no shifts after the first period, though he remained on the bench.
Coach John Tortorella said last week he believed Dubois wanted to leave the Blue Jackets. The forward signed a two-year contract Dec. 31.
"I've told you many times, I really don't make decisions as far as minutes, it's up to the player to show me," Tortorella said after the game. "And if there's one thing I'm pretty easy to read on is the minutes. You're going to get out there, if you play and if you play the proper way you're going to get back out there. The onus is on the player and all players, not just the player we're talking about here that sat. It's all the players, and I'm not a hard guy to read as far as that's concerned."
NOTES: The Lightning are the first defending Stanley Cup champions to start a season with three straight wins since the Dallas Stars in 1999-00. The longest such streak is five games by the 1920-21 Ottawa Senators and the 1985-86 Edmonton Oilers. … Tampa Bay forward Steven Stamkos had an assist, giving him six points (two goals, four assists) in a three-game point streak to start the season. … Lightning forward Anthony Cirelli had an assist and has four points (goal, three assists) in a three-game point streak. … Bjorkstrand has five points (two goals, three assists) in a three-game point streak.