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 from close range. He has nine goals during his streak.
Mitchell Chaffee pushed it to 4-0 with a power-play goal at 14:18, scoring from the slot off a backhand feed by Paul.
Pyythia cut it to 4-1 at 7:23 of the third period with a short-handed goal. Sean Kuraly forced a turnover by Victor Hedman and passed to Pyythia, who scored from the high slot.
Fantilli made it 4-2 at 8:05 when he finished a 3-on-1 rush with a wrist shot, and Sillinger added a power-play goal to pull Columbus within 4-3 at 14:11.