They have lost four consecutive games and been outscored, 29-13, since an Opening Day victory against the Baltimore Orioles.
Lefthander Matt Hall, the latest in what has amounted to a tryout camp for starting pitchers, couldn’t get through three innings. There was little help from the offense as the Sox were 2 for 10 with runners in scoring position.
Now the last-place Sox start a seven-game road trip on Wednesday, again playing the Mets but this time at Citi Field in New York.
Nate Eovaldi is scheduled to face two-time reigning National League Cy Young winner Jake deGrom. What is now a bad start could get worse.
Hall retired the side in order on six pitches in the first inning, aided by a nice running catch toward the line by right fielder Kevin Pillar on leadoff hitter Amed Rosario.
Then Hall needed 35 pitches to get through the second inning as the Mets took a 3-0 lead.
Robinson Cano, who has hit well at Fenway since his early days with the Yankees, drove in the first run with a double to left. Rosario had a two-run single with two outs when Hall left an 0-2 fastball over the plate.
Hall allowed three runs on three hits over 2⅔ innings in his first major league start.
Red Sox starters have lasted only 13⅓ innings in the last four games, giving up 15 earned runs on 17 hits.
Righthander Austin Brice, who was designated for assignment by the Miami Marlins in January, replaced Hall. He managed to get five outs before Jeff McNeil singled in the fifth inning and J.D. Davis lined a fastball off the Pesky Pole to give the Mets a 5-1 lead.
As the Red Sox continued their desperate search for pitchers, 24-year-old lefthander David Peterson pitched with composed efficiency in his major league debut for the Mets, allowing two runs over 5⅔ innings.
Peterson was the first opposing lefthander to post a win making his debut at Fenway since Brian Talley of the Indians in 2002.
Peterson was a 28th-round draft pick by the Sox in 2014 but elected to follow through with his commitment to the University of Oregon. He developed into the 20th overall pick of the 2017 draft for the Mets.
Peterson finished last season in Double A but impressed the Mets enough to get a start at Fenway. He allowed seven hits, walked two, and struck out three.
It took a series of unusual events for the Red Sox to score their first run.
Kevin Plawecki led off the bottom of the third inning with a double to left field. Andrew Benintendi, batting ninth for the first time since 2016, drew a walk.
Jose Peraza followed with a line drive to right center field that ticked off the glove of Brandon Nimmo. Plawecki, watching the play with a foot on second base, advanced only as far as third.
With the bases loaded and no outs, Peterson struck out J.D. Martinez swinging at a slider. Rafael Devers followed with a one-hop ground ball to second.
Robinson Cano flipped to second base to force Peraza. Plawecki then scored while Benintendi was caught in a rundown between second and third.
The Sox did not score again until the sixth inning on doubles by Devers and Pillar.
Peter Abraham can be reached at firstname.lastname@example.org. Follow him on Twitter @PeteAbe.