Colton Parayko scored twice, and Binnington made 31 saves for St. Louis (32-15-9), which is 2-5-2 in the past nine games.
"We've been playing good, we've had our chances," Parayko said. "We're just in the middle of a little bit of a grind right now. That's the way it goes. It's a long season. We have a group in here that knows how to respond and we know what to do. We're in a good spot still. Nothing to be worried about, obviously."
Parayko gave the Blues a 1-0 lead with a power-play goal at 7:18 of the first period and made it 2-0 at 10:49. He has four goals in the past three games after two in his first 46.
"First one was just a good pass by [Vince Dunn]," Parayko said. "Second one was just a good pass by [David Perron]. I was just all alone and just wanted to step into it. I had enough time to let it rip.
"Overall, I'm just trying to get pucks towards the net. Our forwards are doing a really good job of getting to the net and creating second opportunities."
Benn cut the lead to 2-1 on a power play at 17:48 when he redirected Mattias Janmark's pass, and Hintz tied it 2-2 at 13:25 of the second period with a wrist shot from the slot.
"I think we had pretty good looks the whole game, so I think it was a good line today," Hintz said.
The Blues killed off a Jay Bouwmeester holding the stick penalty in the final 46 seconds of the third period and 1:14 to start overtime but couldn't build off the momentum.
"We ended up getting a point," Blues coach Craig Berube said. "We had to kill the penalty there and they scored in overtime."
Stars coach Rick Bowness missed the game due to illness and was replaced by assistant coach John Stevens.
"We went through our normal game day," Stevens said. "We had our meetings this morning and then later this afternoon coming to the rink we got word [Bowness] was taken in just as a precautionary measure."
