Lester allowed two runs or fewer for the eighth start in a row and left after six innings with the lead. The Tampa Bay Rays then rallied for a 6-4 win.
"We made David work pretty hard, but he was able to get a lot more early-out counts than I was tonight, and that's why he was able to go a couple more innings," Lester said.
"To leave up 3-2 against David Price is a good feeling. But they got some good at-bats tonight against Andrew (Miller) and (Junichi Tazawa) and unfortunately, we're on the bad side."
Price won his sixth start in a row and Evan Longoria hit a three-run double in the Rays' eighth straight victory.
Price (11-7) struck out 10 over eight innings. He tied the team record shared by Matt Moore and Scott Kazmir for victories in consecutive starts.
This was Price's first game against Boston since he hit David Ortiz with a fastball on May 30, setting off a verbal skirmish between the stars.
There was no trouble between them this time as Ortiz returned to the lineup, a day after leaving a game because of back spasms. Ortiz hit an RBI single in a two-run sixth for a 3-2 Red Sox lead.
"Who cares? We lost," he said. "(The back) is feeling better. After what we did last night and today when I got up and took some medication, it felt much better."
Ben Zobrist got his fourth hit, an RBI single that made it 3-all in the Rays seventh. Later in the inning, Longoria delivered his go-ahead hit off Tazawa (1-2).
Jake McGee gave up a run in the ninth and got his 10th save.
Desmond Jennings hit a two-run homer in the Rays fifth for a 2-1 lead.
Lester gave up two runs and struck out seven. He had allowed just one earned run over 31 innings in his previous four starts.
Shane Victorino connected in the second for the 20th home run allowed this season by Price. Victorino also singled home Ortiz in the sixth.
"I thought we had a very good approach against (Price)," Boston manager John Farrell said. "Vic swung the bat good, David obviously had some good at-bats against him. We came back twice against him to take the lead in a 3-2 ballgame, and unfortunately the seventh inning unfolded the way it did."
NOTES: Boston C Ryan Lavarnway (wrist) was sent to Triple-A Pawtucket to continue his rehab assignment. ... Tampa Bay plans to recall RHP Jeremy Hellickson (elbow surgery) from Single-A Charlotte to make his second big league start of the season Saturday night. The Red Sox will counter with RHP John Lackey.