Lee (0-4) allowed five runs and six hits in seven innings. The 2008 AL Cy Young Award winner hasn't won a game since last Sept. 26, or 273 days ago. Lee is making $21.5 million this year, most on the Phillies.
In the opener, Carlos Pena hit a three-run homer in the eighth inning and the Rays held on for a 3-2 victory, making David Price the first AL pitcher to reach 10 wins.
Cole Hamels pitched three-hit ball for seven shutout innings in his first appearance against the Rays since he was the MVP of the 2008 World Series. But the lefty departed after throwing 111 pitches and Pena connected off Antonio Bastardo (2-2).
Because of Friday's rainout, the Rays went with a "bullpen" game. Cesar Ramos tossed 2 2-3 hitless innings in his third career start and first since 2009. Wade Davis allowed three runs and three hits in 2 2-3 innings in relief of Ramos. Brandon Gomes (2-2) earned the win with 2 2-3 scoreless innings.
The five-time defending NL East champion Phillies are 6-15 in June and fell back into last place, a game behind Miami.
The depleted Phillies should be getting some help soon. Chase Utley is scheduled to play for Triple-A Lehigh Valley on Tuesday, and the five-time All-Star second baseman could make his season debut this week. Utley has been sidelined because he has chronic knee problems.
Former NL MVP Ryan Howard is still rehabbing in extended spring training after having surgery to repair a torn Achilles' tendon last year. Two-time Cy Young Award winner Roy Halladay hasn't pitched since May 27 because of a lat injury.
Lee hasn't received much run support this season. He couldn't even get a win when he threw 10 scoreless innings at San Francisco on April 18. But he's also blown three three-run leads. In his last seven starts, Lee has a 5.10 ERA.
Sean Rodriguez hit an RBI double off Lee to put the Rays up 1-0 in the second. Conrad followed by hitting a 3-0 pitch down the left-field line to score two and make it 3-0.
Placido Polanco hit an RBI double and John Mayberry Jr. followed with a run-scoring single to get the Phillies within 3-2 in the fourth.
Lee retired the first two batters in the sixth before Ben Zobrist singled and Rodriguez walked. Conrad then hit a double off the top of the fence in right-center to give the Rays a 5-2 lead.
Rodriguez knocked over catcher Brian Schneider on a play at home. Schneider left the game with a right ankle sprain.
Polanco's RBI double in the sixth cut it to 5-3. But the Phillies couldn't score him from third with no outs.
The Rays got two insurance runs in the eighth when B.J. Rosenberg walked four batters. Jake Diekman came in and also walked in a run.
Price (10-4) went seven innings in Game 1 and gave up four hits, including Jimmy Rollins' homer in the sixth.
"I try to treat every start the same but whenever you're facing somebody who is one of their top guys, it definitely heightens your sense of awareness," Price said. "You know you can't go six and give up three."
Phillies manager Charlie Manuel became testy with the media when questioned about lifting Hamels for Bastardo, as well as explaining his late-game pinch-hitting decisions.
"That's our eighth-inning guy," Manuel said of Bastardo. "I think right now, what you see is the pitchers that we have. That's the ones that we have in our minor leagues and up here. That's what it is."
"You guys ought to sit in the dugout with me and give me all the scenarios," Manuel added. "I don't think we know them. I mean, we don't know how to manage the game. Like really, I think you should sit down there with us or tweet us (strategy) or something."
A duel between two of the top left-handers in the major leagues shaped up from the start. Price trailed 1-0 before the Rays rallied.
Fernando Rodney pitched a scoreless ninth for his 21st save in 22 chances. Rollins reached second base with two outs after a single and stolen base, but Rodney struck out Hunter Pence swinging to end the game.
Hamels was 1-0 with a 2.77 ERA in two starts against Tampa Bay in 2008 when the Phillies won their title. He pitched even better on Sunday.
Bastardo walked two of the first three batters he faced. Pena hit the first pitch over the fence in right field.
NOTES: Lee is the only pitcher in the majors this season with at least 10 starts and no wins. ... Jim Thome, pinch-hitting for the Phillies in the eighth in Game 1, was intentionally walked to tie Mickey Mantle for seventh place on the career list with 1,733 walks. ... Hamels fanned seven to tie Hall of Famer Jim Bunning for sixth place on the Phillies' career strikeout list with 1,197. ... The Phillies' sellout streak is up to 257 straight games, counting postseason play. ... The Rays open a three-game series at Kansas City on Monday night with RHP Alex Cobb (3-3, 3.82 ERA) scheduled to face Royals RHP Luke Hochevar (4-7, 5.65). ... Philadelphia hosts the Pirates on Monday night for the first of four when RHP Joe Blanton (6-6, 5.04) faces LHP Erik Bedard (4-7, 4.13).