Malkin also scored, and Marcus Pettersson had a goal and an assist for the Penguins (28-21-9), who were outscored 21-10 during their losing streak. Tristan Jarry made 25 saves.
"I thought it was a hard-fought game," Pittsburgh coach Mike Sullivan said. "I loved our will to win. We generated a fair amount of scoring chances. I don't think we got rewarded for some of our effort out there. I thought the Blues played hard. I thought their goalie played really well. There's a fine line between winning and losing in this league. It could have deflated us when they scored late in the game. Our effort was strong in the overtime."
Jordan Binnington made 45 saves for the Blues (26-28-5), who have lost five in a row (0-3-2) and have been outscored 21-8 during that span. Justin Faulk had a goal and an assist.
"[Binnington] played great, especially that first period," Faulk said. "I think we gave up 25 shots, or whatever it was (21). He stood tall and gave us a chance, more than a chance.
"I thought in general we played more of a competitive hockey game tonight. Obviously, heavily outshot in the first, but I think we battled in the second and third. We had a little bit more there. We pushed the OT there, but (it) kind of becomes a little bit of a crapshoot once it gets there with 3-on-3 hockey."
St. Louis was looking for a better response after some harsh comments from coach Craig Berube following a 3-2 overtime loss to the Vancouver Canucks on Thursday.
"I thought that we got a good response tonight. Competitive," Berube said. "We were physical. Played hard. Just offensively, we've got to get more done. But overall, I was pretty pleased with the effort."
Pettersson's first goal of the season gave the Penguins a 2-1 lead at 14:32 of the third period, scoring from the slot with a wrist shot off a rush.
Faulk tied it 2-2 at 17:33 when he jammed the loose puck through a crowded crease after forward Alexey Toropchenko took it hard to the net.
"We were down and bodies laying down there, just kind of in a normal situation, you don't go in there and kind of sniff around for something being down one," Faulk said. "You just kind of went to the net and hope you can find it on the weak side. It just squirted free just enough to get a little bit on it."