The San Francisco Giants right-hander caught Zobrist looking at a third strike, and he wound up pitching into the eighth inning for a 6-4 victory in a series opener at Wrigley Field.
"It was good to have a battle like that, it kind of gets you locked in especially being able to come out on top," said Black, who finally ran into trouble in a four-run Cubs eighth. "It gets you focused and be like, 'OK, I can execute pitches and get some guys out.'"
Blach (2-2) got quick support with runs in four of the first five innings, including a leadoff home run by Joe Panik.
"To jump on the board early, it was cool," said Panik, who went 3-for-4 with his first career leadoff homer. "I felt good, I was seeing the ball well, the swing path was good. Hopefully this is the start of some good things."
Panik added a third-inning RBI double.
Brandon Belt (2-for-5) and Justin Ruggiano (2-for-4) also hit solo home runs for San Francisco. Ruggiano's blast to left came in the eighth inning off Hector Rondon, the Cubs' third pitcher of the night, and gave the Giants a 6-0 lead.
The Giants (20-26) made it eight wins in their past 10 games while the Cubs (22-21) fell for the second time in their past three.
Cubs pinch hitter Ian Happ then tripled to deep center, and Blach was pulled in favor of right-hander Derek Law. The Cubs added two runs as Zobrist hit a two-run homer to right off Law , trimming the deficit to 6-4.
Hunter Strickland, the fourth Giants pitcher of the inning, got Willson Contreras to roll into an inning-ending double play.
Blach allowed three runs on seven hits and struck out three with no walks in seven-plus innings.
"That's a tough night to pitch," Giants manager Bruce Bochy said. "The ball was just flying out. He probably got a little tired in the eighth, (but) he really set the tone, and our guys did a nice job swinging the bat."
Giants closer Mark Melancon faced four batters in a scoreless ninth for his ninth save.
Cubs starter John Lackey (4-4) worked five innings -- his shortest outing of the season -- and took his first loss since April 23. Lackey gave up five runs on seven hits while striking out six and walking a pair. He allowed two homers and hit two batters.
"Honestly, I threw the ball better tonight than my last three," Lackey said. "I felt like I executed quite a few pitches, but they got a few more balls up than we did."
It was San Francisco's first visit to Wrigley Field since the 2016 National League Division Series, won in four games by Chicago en route to a World Series championship.
Panik slugged his second homer of the year as the Giants claimed a 1-0 first-inning lead. The shot off Lackey came on a full count and narrowly cleared the left field basket.
Panik struck again in the third, doubling home Gorkys Hernandez with one out for a 2-0 lead. The Giants second baseman then scored from second on Belt's two-out base hit to left for a 3-0 advantage.
The Cubs threatened in their half of the third when Zobrist tripled to right-center with two outs. Zobrist reached base in a 20th consecutive game dating to April 28, but he was stranded when Albert Almora Jr. grounded to short to close the inning.
Ruggiano's double to right with no outs in the fourth plated Eduardo Nunez for a 4-0 Giants lead, while Belt got in the scoring parade with a leadoff homer to left in the fifth to make it 5-0.
"They took advantage of the wind tonight and we didn't," Cubs manager Joe Maddon said.
NOTES: The Giants were 1-5 at Wrigley Field last season and are now 2-9 against the Cubs over their past 11 in Chicago. ... Giants OF Denard Span will be out at least until Wednesday due to a sprained left thumb he sustained Sunday at St. Louis. ... The Giants send RHP Johnny Cueto (4-3, 4.50 ERA) against Cubs LHP Jon Lester (2-2, 3.57 ERA) in Tuesday's second of a four-game series. ... Chicago's rainout last Saturday against the Milwaukee Brewers has been rescheduled for July 6 at Wrigley Field, an open date for both teams. ... The Cubs called up LHP Zac Rosscup from Triple-A Iowa while RHP Jake Buchanan was designated for assignment. ... LHP Brett Anderson remains on the disabled list (back strain), but Cubs manager Joe Maddon said he is progressing toward a return. However, Maddon did not specify how soon that might occur.