Mikael Pyythia, Adam Fantilli and Cole Sillinger scored for the Blue Jackets (12-15-5), who are 0-3-2 in their past five games. Kirill Marchenko had two assists, and Jet Greaves made 27 saves.
"We were very frustrated after two (periods) with the way we were competing, the way we were battling, the way we were soft and looked like we were intimidated for whatever reason," Columbus coach Dean Evason said. "It's easy to respond when you get into a situation like that and you're prodded a little bit. Are we happy with the response? Absolutely. ... We don't question how hard our group is trying to work, but for two periods ... there's no reason why you don't start that way."
Luke Glendening gave Tampa Bay a 1-0 lead at 3:21 of the first period when he redirected a shot from Nick Perbix.
Paul extended the lead to 2-0 at 1:28 of the second period after he won a puck battle against Sillinger near the right boards and scored from the high slot.
Guentzel made it 3-0 at 7:36, stuffing in his own rebound. He has nine goals during his streak, which is the longest by any player this season.
"First two periods were really good and then we kept taking too many penalties," Lightning captain Victor Hedman said. "That costs us a few. End of the day we got two points. After a long road trip, coming home and getting a win is big."