Okposo made it 2-0 by tipping a pass in front at 8:54 of the second.
Buffalo did not have another shot on goal until a slap shot from Rasmus Dahlin at 12:07 of the third period.
"We just came out flat (in the third)," Okposo said. "We had a tough power play to start there, a couple tough power plays to start. It just killed any momentum we had built in the first two periods. Made them feel good. We just have to do a better job of being a little bit harder and being a little bit simpler.
"When we have a chance to probably close out a game at the start of the third there, we just have to come out better."
Jeff Carter nearly cut it to 2-1 with a wraparound at 16:31 of the second, but Tokarski pushed to his right for a pad save at the left post.
"Play our game," Carter said. "When we play like that, we're very hard to play against. We've shown that a lot this year. At times, we haven't. It's pretty noticeable. So we had a lot of opportunities tonight. Their goalie played an outstanding game. We'll take some positives, but we've got to start getting some points here."
Teddy Blueger had a chance for Pittsburgh on a breakaway 1:10 into the third, but Tokarski made a glove save on his snap shot.
Jake Guentzel had a pass from Bryan Rust go in off his skate, cutting it to 2-1 on a power play at 5:59 of the third. Crosby had the secondary assist.
"I'm glad we had a two-goal lead and we had [Tokarski] in net. That's what I think of the third period," Sabres coach Don Granato said. "It was [Tokarski's] show from that point. Starting right away. … We were reeling all the way through but battled all the way through."
NOTES:Tokarski's previous NHL high was 44 saves against the New York Rangers on April 1 last season. … The Sabres were 0-for-5 on the power play. The Penguins were 1-for-4; they hadn't scored on 28 straight chances before Guentzel's goal. … Pittsburgh is 4-4-2 at home. It was 22-4-2 at home last season.