Calvin de Haan and Alex DeBrincat scored, and Kevin Lankinen made 38 saves for the Blackhawks (24-35-10), who lost their fourth straight, including 4-0 at the Florida Panthers on Thursday.
"That's a good hockey team that team can turn it on offensively and they can shut it down with the best of them," Chicago coach Derek King said. "Eventually, that's the kind of the team we want to be. Obviously we're not there."
Stamkos gave the Lightning a 1-0 lead at 6:11 of the first period with a one-timer from the left face-off circle off a backhand pass from Point.
Point extended the lead to 2-0 at 10:12 from the low slot off a pass from Kucherov.
De Haan cut it to 2-1 at 12:11 with a shot from the point.
"I've been putting a lot of pucks at the net and they just haven't gone in or we're not whacking in rebounds," de Haan said after scoring his third goal in 63 games this season. "It feels like it's a little too late to be honest. Maybe if some of those went in at the start of the year it might have added up to a few more points for our team."
DeBrincat tied it 2-2 at 17:21 with his 39th goal of the season on a wrist shot from the slot off a pass from Seth Jones.
"I will give our guys credit," King said. "Back-to-back road [games]. We stayed with it. We tried, it's not from a lack of effort."
Tampa Bay pulled away in the final two periods behind the newly formed line of Colton, Paul and Brandon Hagel.
"That was their best game since they've been together," Cooper said. "When you're trying to find chemistry with a line it takes some time, but I thought they found their stride tonight. Their work ethic. They were just doing a ton of the right things that we preach."
Colton put Tampa Bay ahead 3-2 at 6:12 of the second period on the rebound of an Erik Cernak shot.
"These first couple of games we've been trying to form an identity and I think you saw that a little bit tonight," Colton said. "We had to bounce back. Last game I think we were [minus-2]. Can't be having that happen, so it was nice to get rewarded."
Colton then made it 4-2 at 12:15 off a between-the-legs pass from Paul.
"My game is work hard first, but I mean, I've still got a little bit of skill," Paul said. "It was a great play by him going to the net."