Bourque got the Predators back into it when Matt Irwin failed to keep the puck in at the blue line on the power play. Bourque raced to the loose puck and beat Niemi for the goal.
But Niemi and the Sharks held on for the win.
Sharks general manager Doug Wilson criticized his team for passing too much instead of shooting the puck, and the message clearly got through as they put 16 shots on net in the opening period to take a 1-0 lead.
"We knew they were a fast start team," Nashville coach Barry Trotz said. "We knew they were going to throw a lot of pucks at the net. That was stated by their team management and coaches. We had to get through that first period. They jumped on us early and got zone time."
Rinne stopped all but one but was screened by Pavelski on Boyle's slapper from the point 19 seconds after Kevin Klein was sent to the penalty box for slashing Logan Couture. The goal was the first for Boyle since the second game of the season and the first for any Sharks defender since Irwin scored on Jan. 26 against Edmonton.
"I'm just glad I got it through," Boyle said. "It's been tough this year getting the pucks through. We got a break. I think the guy lost a stick, broke a stick and we got to move it around a little bit. Pavs obviously a great screen in front. That was the key there and I got my shot through."
NOTES: Nashville F Brandon Yip left in the first period with an upper body injury after crashing into the boards. ... The Predators failed to earn a point for just the second time in 11 games against the Sharks. ... Thornton got his 1,100th career point with an assist on Pavelski's goal. ... San Jose has only five goals from its defensemen all season. ... Sharks F Marty Havlat left the game in the third period with an undisclosed injury.