Greiss, starting in place of regular goaltender Antti Niemi, frustrated the Capitals by blocking 39 shots, many of them from point-blank range.
The Sharks, who lead the Los Angeles Kings by three points in the division, lost to St. Louis 3-0 on Sunday to open a nine-game road trip.
"We wanted that first win yesterday and didn't get it," said Pavelski, who also had two assists against the Capitals. "You don't want to go 0 for 2 in a nine-game road trip. You take the wins when you get them."
Washington have now lost 16 of their last 17 games against San Jose and missed the chance to leapfrog slumping Toronto into the eighth and final playoff spot in the Eastern Conference.
The Sharks converted three of six power plays, while Washington was scoreless in four.
"Their power play is good," said Capitals forward Matt Hendricks. "They have a lot of weapons out there. They weren't so much your typical power-play goals but they got pucks to the net and found ways to get them in.
"We penalty killers need to be better. The onus is on us to help our goalie out. We left him out to dry a couple of times."
The Sharks opened the scoring in the first period when Dan Boyle fired a shot from beyond mid-ice that was re-directed by Pavelski at the blue line.
With the puck bouncing along the ice, Capitals netminder Braden Holtby managed to get a glove on it but could not hold on and watched in horror as it slid into the net.
"I'd probably liked to have been out further but at that point I'm trying to make sure I'm in the right position," Holtby said. "It happened pretty quick to me. I wasn't expecting that."
Pavelski poked in a rebound early in the second period on the power play to give the Sharks a 2-0 lead and silence the crowd of nearly 19,000 at the Verizon Center.
Marleau scored on a rebound, his 21st goal of the season, to give the Sharks a 3-0 before Dmitry Orlov countered for the Capitals with less than a second left in the period.
Third-period goals by Sharks defenseman Brent Burns and another by Marleau hiked the lead to 5-1 with 12 minutes left, sending the crowd scurrying for the exits.
Roman Hamrlik and Jeff Schultz scored to cut the Sharks' lead to 5-3 with five minutes left but the Capitals could not get any closer.