SAN FRANCISCO -- With their rotation depleted by injuries, the Giants have been leaning heavily on their bullpen to cover innings and help them get by until reinforcements arrive.

The unit held strong on Tuesday night, when Randy Rodríguez, Sean Hjelle, Taylor Rogers, Ryan Walker, Tyler Rogers and Camilo Doval combined to allow only four hits in the Giants¡¯ 5-1 win over the Cubs at Oracle Park.

Rodr¨ªguez served as the opener and struck out five over 2 2/3 innings in his first career Major League start, using his electric fastball-slider combination to rack up 10 swinging strikes. The 24-year-old rookie began his outing with two scoreless innings, though he allowed the Cubs to get on the board in the third after issuing a two-out walk to Nico Hoerner, who promptly stole second and scored on Michael Busch¡¯s RBI single to right field.

¡°Randy went out there and he set the tone for the game,¡± Hjelle said. ¡°He did his job and then some. You don¡¯t want to be the guy that kind of stops that train from rolling. You just want to pass the ball on to the next guy when your job is done.¡±

That proved to be the extent of the damage against San Francisco¡¯s relief corps, as Hjelle, the Rogers twins, Walker and Doval put up zeros the rest of the way to help the Giants win back-to-back bullpen games and take the first two games of this four-game series.

¡°Special,¡± said Hjelle, who lowered his ERA to 2.39 through 25 appearances this year. ¡°I think as a collective unit, it¡¯s been really fun to be a part of this year and be down there. I feel like guys are ready all the time in any situation. Nobody¡¯s really shying away from innings. It¡¯s really fun to be a part of right now.¡±

San Francisco¡¯s relievers outdueled veteran right-hander Kyle Hendricks, who tossed seven innings of two-run ball for Chicago. The Giants opened the scoring in the second inning, when Jorge Soler singled and Matt Chapman worked a 13-pitch walk to set up Michael Conforto¡¯s RBI single to right field. David Villar followed with a sacrifice fly to left to extend San Francisco¡¯s lead to 2-0.

The Giants tacked on a trio of insurance runs in the eighth behind Soler¡¯s sacrifice fly and Chapman¡¯s two-run single to left, giving some much-needed breathing room to Doval, who delivered a 1-2-3 ninth to end the game.

¡°If we just add on a run or two there at that time, the way the game went, it felt like 10,¡± manager Bob Melvin said. ¡°To get three was obviously huge.¡±

The Giants hoped to get away from regularly using bullpen games this year, but the injuries to Blake Snell (left groin strain), Kyle Harrison (right ankle sprain), Keaton Winn (right elbow inflammation), Robbie Ray (Tommy John surgery) and Alex Cobb (left hip surgery) have left them scrambling to fill the gaps in their rotation. Most of that workload has been passed on to the bullpen, which is only one-third of an inning behind the Brewers for the most innings pitched (329 2/3) in the Majors this year.

Walker (2.23 ERA) and Tyler Rogers (2.92 ERA) are tied for the Major League lead with 40 appearances this season, though they¡¯ve remained effective and established themselves as reliable bridges to Doval. Melvin has expressed some concern over their workload, which he recently described as ¡°extreme,¡± but the Giants hope to take some of the pressure off their bullpen once they start getting some pieces back in their rotation.

Snell and Harrison likely won¡¯t be options to rejoin the roster until next month, but the Giants could get a more immediate lift from No. 6 prospect Hayden Birdsong, who will be called up from Triple-A Sacramento and make his Major League debut on Wednesday.

Birdsong will join Logan Webb and Jordan Hicks as the only traditional starters on the Giants¡¯ roster, leaving two more rotation slots for the bullpen to fill in the meantime.

¡°It feels like it happens every year for every team where you run through a stretch like that and it always finds a way to work itself out,¡± Hjelle said. ¡°Everybody is ready in any situation down there. ¡­ We want to pitch, we want to grab the ball. It¡¯s what we dream of.¡±