LOS ANGELES — With more than one-fourth of the season in the books, Braves rookie reliever Brandon Cunniff still had not allowed a hit by a right-hander batter and had a majors-best .044 opponents’ average overall before Monday night’s series opener at Dodger Stadium.

Righties were 0-for-30 with six walks and seven strikeouts against him, while lefties were 2-for-15 with two walks and seven strikeouts. The hitless streak against right-handed batters is the second-longest for any pitcher to begin his career since at least 1974, the first season that such records are kept by STATS, Inc. Kansas City’s Bob McLure had an 0-for-33 streak to begin his career in August-September, 1975.

“I don’t know, I’m just throwing the ball,” said Cunniff, as unassuming and quiet a ballplayer as you’re likely to come across. “The defense is playing really well, too.”

Cunniff was 2-0 with a 1.80 ERA in 17 appearances before Monday, allowing two hits, three runs and one homer in 15 innings, with eight walks and 14 strikeouts. Hitters were 1-for-13 against him with runners in scoring position and 1-for-16 in the late innings of close games.

Not bad for a 26-year-old rookie who spent 2 ½ seasons in independent-league baseball after being released by the Marlins during his first minor league season in 2010.

“I think anybody that’s come from independent ball is hanging onto their dream; that’s enough said,” Braves veteran closer Jason Grilli said. “They believe in themselves. So, kudos to him for what he’s doing, to come up here and jump right in the mix and do his thing. He just wanted and chance and he got it. It’s exciting to see, man, for a kid to get a chance. This kid is figuring himself out at this level, and it’s pretty impressive.”

Cunniff was sent back to Triple-A after a heavy workload to start the season, including 10 appearances in the Braves’ first 15 games, capped by three consecutive outings April 21-23, the last one a five-out appearance.

The right-hander gave up a solo homer May 8 at Washington in his first appearance after returning from Triple-A, but allowed no hits in five scoreless innings over his next six appearance before Monday.

After giving up six walks in first 10 appearances, Cunniff walked only two batters in seven appearances since returning from Triple-A.

“Yeah, definitely the rest helped,” he said. “My body feels amazing. It helped a lot. Just the rest.”

Braves manager Fredi Gonzalez said last week that Cunniff, because of his performance so far, would be considered for more high-leverage situations with games on the line.

“That’s awesome,” Cunniff said. “That’s what I want to do. I want the high-pressure situations. All of us do.”

He led NL relievers in fewest base runners allowed per nine innings (6.0), and was tied for fifth in the NL in percentage of inherited runners stranded (93.3, 14 of 15 stranded), just behind teammate Luis Avilan (93.8, 15 of 16 stranded).

Cunniff also led the majors in first-batter efficiency, holding first batters hitless in 12 official at-bats, and had not allowed a hit in seven road appearances before Monday.