It remains to be seen how long the winless Jeff Samardzija will remain in Chicago, which has provided baseball's ERA leader with very little support.
The Giants go for a fifth consecutive win as they open a three-game home set against the NL-worst Cubs on Monday.
It's been quite a turnaround for San Francisco (32-18) after finishing 10 games below .500 last season. The Giants are third in the majors with 59 homers and own the third-lowest ERA at 3.05.
"We got a good team, better than a lot of people realized at the start of the year," Madison Bumgarner told MLB's official website. "We play together. On paper it may not be the best team, but I'd put us against anybody. We don't have anyone who's selfish. We play as a complete team."
Morse has been a big part of San Francisco's success with team highs of 10 homers and 33 RBIs. The veteran slugger delivered three doubles and drove in four runs as the Giants swept Minnesota with Sunday's 8-1 victory.
Giants fans gave Morse a loud ovation when his face appeared on the scoreboard.
"Moments like that make you feel so humble and happy that you're here," said Morse, signed to a one-year deal in December. "Every day feels like the playoffs here. It's awesome."
Morse will try to stay hot against Samardzija (0-4, 1.46 ERA), who hasn't been able to catch a break thus far. The right-hander is looking to snap a 16-start winless drought dating to August, a stretch during which he's received an average of just 2.48 runs of support.
"He's the best pitcher in the league right now - American League, National League, Japanese league," second baseman Darwin Barney said. "The wins will come. It's one of those funny things. ... We're trying hard. Maybe we're trying too hard for him."
Samardzija was in line for the victory after throwing seven scoreless innings against the Yankees on Wednesday, but Hector Rondon blew the save in the 4-2, 13-inning defeat.
"You take it with how it goes. It doesn't always go the right way," said Samardzija, who could be traded before the deadline. "We're not wasting anything. With modern technology, every game pretty much gets seen and watched. I don't think it's any secret with what I'm doing. I can get better. I'm doing some things that are good. Let's keep building on that."
Samardzija is 0-1 with a 2.70 ERA in seven games - two starts - against the Giants. He'll be opposed by Yusmeiro Petit (3-1, 4.76), who is set to fill in for the injured Matt Cain again.
"It's part of my job," Petit said. "Emergency starting is difficult. But I've done it a lot, so it makes it easier."
Petit's last two emergency starts haven't gone well, though. After yielding a career-high eight runs over 4 1-3 innings at Pittsburgh on May 5, the right-hander was tagged for five runs in as many innings against Miami on May 16.
Petit is 2-1 with a 5.23 ERA in six games - four starts - against the Cubs, though he hasn't faced them since 2009.
Chicago (18-30) just split a four-game set at San Diego after falling 4-3 on Sunday. Junior Lake and Starlin Castro both homered for the Cubs, who have yet to win a road series.
"Did we want to take the series? Absolutely," manager Rick Renteria said. "But we knew it was going to be difficult. We're seeing some good things."
The Cubs took four of seven from the Giants last year, including all three meetings in San Francisco by a combined 6-3 margin.