Musgrove (8-0) permitted two runs and five hits, struck out a season-high nine and walked one. The 6-foot-5 right-hander has allowed two earned runs or fewer in each of his 12 starts this year.
''He's one of the best pitchers in major league baseball right now, the way he's moving pitches, the way he's locating very good,'' Cubs catcher Willson Contreras said. ''We had a couple chances but weren't able to come through.''
San Diego improved to 7-2 in its last nine games with its first four-game series sweep of Chicago since Aug. 16-19, 2010, at Wrigley Field. The Padres' 41-24 record matches their best 65-game start since 1998, when the club won the NL West and advanced to the World Series.
The Cubs have been outscored 90-28 during their longest slide since they lost 12 consecutive games from Aug. 5-16. They have held leads in seven of the 10 straight losses.
''I don't try to find similarities, but this one just feels a little like we don't have that guy coming back around to stop things,'' Cubs manager David Ross said.
Cubs rookie Christopher Morel led off the first with his second homer in as many games, but Matt Swarmer (1-2) was knocked out in the fourth.
San Diego went ahead to stay with three runs in the second. Nomar Mazara hit a two-run drive for his first homer with the Padres, and Jake Cronenworth added an RBI double.
''I've been feeling pretty good at the plate, but I was looking for that, too, for that first (home run),'' Mazara said. ''Finally happened, and I'm grateful for it.''
Mazara has five hits and seven RBIs in his last three games.
''A pleasant surprise,'' said acting manager Ryan Flaherty, who is running the Padres while Bob Melvin is sidelined due to COVID-19 protocols.
Manny Machado made it 4-2 with an RBI single in the fourth, and Jurickson Profar homered off David Robertson in the eighth. Machado had three hits.
Musgrove allowed one hit after Morel's single with two out in the second. His 1.59 ERA trails Tony Gonsolin of the Dodgers for the NL lead. Musgrove improved to 3-0 with a sparkling 0.82 ERA in three starts on five days' rest this season.
Taylor Rogers allowed a run in the ninth before finishing his 20th save in 23 chances.
Ian Happ had an RBI double for Chicago (23-40), and Andrelton Simmons also drove in a run. Swarmer walked five in 3 2/3 innings.
The Padres improved their major league-best road record to 24-11.
SUPPORT FOR ROSS
Cubs President of Baseball Operations Jed Hoyer reinforced his support for Ross amid the losing streak.
''I think he's done a great job,'' Hoyer said. ''Our conversation is how to make guys better.''
Hoyer wouldn't say whether attempts to build the ''next great Cubs team'' have regressed. ''I'll have a better answer for that later in the season,'' Hoyer said.
Padres: LHP Adrian Morejon was activated from the COVID-19 injured list. LHP Ryan Weathers was optioned to Triple-A El Paso.
Cubs: RHP Adrian Sampson was selected from Triple-A Iowa. LHP Eric Stout was designated for assignment.
Cubs: RHP Marcus Stroman (shoulder inflammation) and LHPs Wade Miley (shoulder strain) and Drew Smyly (oblique strain) are on the 15-day IL, and Hoyer said Stroman is the closest to returning, although Stroman hasn't resumed throwing yet. ''Hopefully weeks,'' Hoyer said of his return.
Padres: LHP MacKenzie Gore (4-2, 2.50 ERA) faces the Rockies on Friday night at Coors Field. Gore allowed six runs in 2 1/3 innings of a 6-2 loss to the Rockies on Saturday.
Cubs: RHP Keegan Thompson (6-2, 3.67 ERA) pitches Friday against the Braves at Wrigley. Thompson was tagged for five runs and recorded two outs in an 18-4 loss to the New York Yankees on Sunday.
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