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5/6/2014 7:20 P.M. ET

Huff may begin rehab assignment Thursday

PITTSBURGH -- Giants left-hander David Huff, who is recovering from a strained left quad, threw bullpen sessions Friday and Sunday in Atlanta. He tossed another bullpen session Monday in Pittsburgh and could be close to going out on a Minor League rehab assignment.

He was 1-0 with a 3.86 ERA in eight relief appearances when he went on the disabled list retroactive to April 21.

"I had an extended game simulated bullpen," Huff said. "It felt great, I think I ended up throwing like 70 some pitches. Monday was Day 13. I feel good about the way things are progressing."

"He had to run curves today," Giants manager Bruce Bochy said. "I haven't talked to Dave Groeschner our trainer yet, to see how he came out of that. Huff feels great, he'll do some pitchers' fielding practice in the outfield and there's a good chance he could begin his rehab on Thursday in Triple-A."

To ease strain on bullpen, Kontos recalled

PITTSBURGH -- In the wild 11-10 win over the Pirates on Monday night, the Giants had to use seven pitchers in the 13-inning affair. That put some limits on pitcher availability Tuesday night in the second game of a three-game series.

To ease the strain on the bullpen, reliever Jake Dunning is back at Triple-A Fresno. Former bullpen stalwart George Kontos is up in his place.

"He's had a couple days off," Giants manager Bruce Bochy said of Kontos. "He has experience up here, he's pitched better than the numbers indicate, he's had some tough luck. That's why he's up here."

Kontos had a 4.91 ERA in 18 1/3 innings at Fresno, with 28 strikeouts. He's a different pitcher than the past couple of years, when he relied heavily on his slider.

"I've been throwing the ball real well," Kontos stated. "I've been snakebitten a little bit with some goofy plays, giving up a couple of runs that way. But as far as throwing the ball, I've been throwing the ball where I want to throw it.

"Velocity has really come back this year, and with the addition of the cutter and the changeup, I haven't really been showing the slider as much, and when I do throw it, guys are swinging and missing, which I think has accounted for the high tally of strikeouts that I had down there. I've been throwing the cutter early and finishing them off with the slider."

Reliever Santiago Casilla had a 14-pitch battle with Neil Walker before striking him out Monday night. Casilla was the only San Francisco reliever unavailable Tuesday.

Worth noting

• Monday night marked the second time the Giants won a game this season when allowing 10 or more runs. Entering the year, they had won just 21 such games dating back to 1958.

• With Monday night's victory, the Giants improved to 9-6 in one-run games. The nine wins are the most in the Majors.

George Von Benko is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.