Elliott made 26 saves in his first start since March 12, a 4-1 loss to the Edmonton Oilers. His last win was against the Red Wings, 3-1 on March 4.
"He was just fantastic, I thought, especially early on in the game," Point said. "He was a difference-maker out there."
Oskar Sundqvist scored, and Nedeljkovic made 34 saves for Detroit (26-31-8), which has won two of its past 11 games.
"I thought we were the better team for two periods and probably the better team all game at [5-on-5]," Nedeljkovic said. "But we're way past the part of the season where we are thinking about good wins or how we measure up against the Lightning.
"We're [22] points out of a playoff spot when we should be contending for one, and this is a game we should have won. Nothing else matters."
Sundqvist made it 1-0 at 8:41 of the third period with a quick shot from between the circles. It was his second goal in three games with the Red Wings after being acquired in a trade with the St. Louis Blues on Monday.
"I thought there were parts of the game where we did good stuff," Detroit coach Jeff Blashill said. "We defended pretty well against a pretty high-octane team. We didn't create enough chances. There were parts of the game where we could have had more net presence."