Colorado won Game 4 in overtime, 3-2. Tampa Bay now trails the series 3-1.
Kucherov and Paul were both hurt during the Lightning's 6-2 victory in Game 3 on Monday, putting their availability for a critical Game 4 in question.
On Wednesday, Kucherov had nearly 23 minutes on the ice, taking two shots, while Paul was on the ice for almost 15 minutes.
Point has been trying to come back from a lower-body injury suffered in Game 7 of Tampa Bay's first-round series against Toronto. The Lightning's center missed over a month before suiting up in Game 1 and Game 2 of the Cup Final. Point was clearly still slowed by the ailment, even in a decreased role, and did not appear in Game 3.
He is day-to-day for now, and Cooper remains hopeful the Lightning haven't seen the last of Point in this Cup Final.
"I haven't ruled him out for the series," Cooper said. "But he's out for [Game 4]. It's a lot of the same things [he's been dealing with]."
Veteran forward Riley Nash entered Tampa Bay's lineup in Game 3 with Point out. He's expected to draw in again Wednesday on the Lightning's fourth line.