SAN DIEGO — The 1962 New York Mets are no longer the sole standard for Major League Baseball futility after the Chicago White Sox lost their 120th game Sunday 4-2 to the San Diego Padres. The Sox and Mets share the modern-day record for most losses in a season, a piece of baseball history no team sets out to accomplish. The Mets went 40-120 in their expansion season. The Sox are 36-120 with six games remaining — three at home beginning Tuesday against the Los Angeles Angels and three on the road in Detroit. The 120 losses are the most in American League history. The Sox surpassed the 2003 Detroit Tigers, who went 43-119. A sellout crowd of 45,197 at Petco Park witnessed the Padres stage an eighth-inning rally Sunday. Sean Burke pitched six brilliant innings for the Sox, allowing one run on two hits with eight strikeouts and one walk in his second major-league start and third big-league appearance. He left with a lead. Korey Lee got the Sox going offensively, homering to left with one out in the third for the team’s first hit against Padres starter Yu Darvish. Jurickson Profar tied it with a one-out homer to left in the bottom of the third. The Sox used the long ball to go ahead 2-1 when Miguel Vargas homered to left with one out in the sixth. Sox reliever Prelander Berroa issued a walk to begin the seventh. But it didn’t come back to bite him as he retired the next three batters. The eighth wasn’t as successful. Berroa surrendered a leadoff double down the left-field line to Donovan Solano. Pinch hitter Luis Arraez followed with an RBI double to left against reliever Fraser Ellard to tie the score. Pinch runner Brandon Lockridge advanced to third on a wild pitch and scored on a sacrifice fly to right by Profar to give the Padres a 3-2 lead. Fernando Tatis Jr. followed with a home run to left to help complete the three-game sweep. It’s the 24th time the Sox have been swept this season. The Sox went 1-5 on the trip that included two extra-inning losses. The Sox have found just about every way imaginable to lose on their way to 120. They’ve been shut out 19 times, they have 35 blown saves and entered Sunday 0-78 when behind after six innings, 0-94 when behind after seven and 0-101 when behind after eight. The Sox won just three times in July and four times in August, losing 22 games in both months. The Sox have had three losing streaks of at least 10 games, including a franchise-record 21 straight from July 10-Aug. 5. That slide matched the AL record established in 1988 by the Baltimore Orioles. They came within two of the all-time record held by the 1961 Philadelphia Phillies. The 21-game skid ended Aug. 6. The Sox fired manager Pedro Grifol on Aug. 8, with Grady Sizemore taking over on an interim basis. They made the change at manager and shook up the coaching staff. The roster turnover has led to a franchise-record 63 players participating in at least one game. The one constant has been the losing, which has led to a season that no one will ever forget.