"Real solid effort," Dallas coach Lindy Ruff said. "A little bit of a rough start, we gave up a couple of doozies to Tarasenko, but after that, it was a heck of a game.
"It was who was going to bend the furthest. I thought the third period we had three, four real good looks."
Vladimir Tarasenko had a goal and an assist, Paul Stastny scored a goal, and Elliott made 25 saves for St. Louis.
"They made a good play, cross-ice through a seam and had a heck of a shot ... not much room up there," Elliott said of Eakin's winning goal. "... It almost looks like it goes on the outside of the net and in, that's how close it was. Just regroup and go take a game from their barn."
The Blues expected a much tougher game after defeating the Stars 6-1 in Game 3 on Tuesday, and they got it.
"They're a good hockey team," St. Louis defenseman Alex Pietrangelo said. "They're going to get opportunities. We've got to limit the opportunities. I think the opportunities they were getting, we were giving them. It's on us to make the right plays."
Tarasenko opened the scoring at 10:17 of the first period on a breakaway after being sprung by Jaden Schwartz, beating Lehtonen through his five-hole after the Stars lost control of the puck in the Blues zone. Dallas had six skaters on the ice, but Schwartz was able to send Tarasenko in alone for a 1-0 lead.