Erik Karlsson tied a franchise record by extending his point streak to 12 games, and James Reimer made 26 saves for the Sharks (11-20-7), who play at the Chicago Blackhawks on Sunday.
"Losing [stinks]," San Jose forward Logan Couture said. "You can only continuously say we did good things so many times. We've got to go out there tomorrow night and win a hockey game."
Olofsson gave the Stars a 3-2 lead at 10:45 of the second period, tapping in a backdoor pass from Pavelski. He was playing his third NHL game after being called up from Texas of the American Hockey League on Tuesday.
"In the neutral zone there I just, for some reason, your instincts kind of take over and I'm like, 'I'm going backdoor,'" Olofsson said. "Luckily, [Pavelski] is thinking the same thing right away. He was just waiting, waiting, waiting. [Defense] was sleeping and then tap-in. Hats off to him, that's a play he does in his sleep. For me, it was just go to the hard areas and put it in."