The 31-year-old right-hander is 6-10 overall with a 5.18 ERA, but he's struggled since May 22, going 1-7 with a 6.40 ERA over his last 13 outings.
Wright's turn before his start against the D-Backs was skipped to keep the rotation in order, and the veteran did strike out two batters in one inning of scoreless relief against Colorado on Aug. 4.
He continues to show great velocity and "stuff," but location problems and a flat sinker have spoiled his earlier efforts, which resulted in a 5-3 record and a 3.84 ERA in mid-May.
"Jamey will go into long relief, and we'll see how the whole thing works," said Alou. "Short relief? We're not looking at that right now. His stuff hasn't changed -- he's still throwing hard -- and the curve, I don't know what happened. He hit a few guys in Pittsburgh ... we haven't seen the hard sinker and cutter."
Hennessey will make his first start since July 1, in the nightcap of a doubleheader at San Diego. In that game, he threw six innings of one-run ball, but received a no-decision in the Giants' 7-4 defeat.
The 27-year-old Hennessey was originally beaten out of the fifth starter's spot by Wright, but forged a 3-1 record and 2.80 ERA as an emergency starter prior to the All-Star break.
"Starting is what I want to do," said Hennessey, who said his arm strength should be there Monday. He threw on the side early Friday evening as a final tuneup, and was confident he could last five or six innings.
"As long as I can keep my pitch count down," he said. "If I have 30 pitches in the first inning, it hurts my chances. I'll just try to do the same as I did in San Diego: keep the pitch count down and keep us in the ballgame."
Overall, Hennessey is 4-2 with a 2.93 ERA and one save.
With the switch, right-hander Matt Morris will start Tuesday night at PETCO Park, with Noah Lowry starting Wednesday and Matt Cain on Thursday in the series finale.
Outfielder Moises Alou is batting .294 overall, but is at only .250 on the current road trip and went 1-for-4 in Arizona on Wednesday.
"I'm missing balls, not hitting them on the sweet spot," said Alou, who has also been dealing with a sore left hamstring. "I'm getting frustrated about it. Usually, I don't have any excuse for not swinging the bat better. But you know what? It's part of the game. I haven't gotten things started so the team can get going."
Change at San Jose Muni?
Bobby Evans, the Giants' director of player personnel, said Friday the club hopes to reconfigure the Class A Giants' stadium to make it more equitable for hitters and pitchers.
"We're not going to make it a hitters' park," said Evans, who explained that it's easier to evaluate prospects when park dimensions are balanced.
To that end, Muni's home plate will probably be moved some five feet or so toward center field, much less costly than moving the outfield fences in. The reconfiguration, if approved, will be done during re-sodding in the offseason.
Rookie catcher Eliezer Alfonzo is hitting .289 with nine homers and 25 RBIs overall, but has spurted with a .364 mark during the road trip and has hit .325 with runners in scoring position.
But can Alfonzo, who has started 44 of 61 games, stay hot during the long grind? Manager Alou said the 27-year-old freshman will play as many as 10 straight games to determine his durability, and he plans to only start backup Todd Greene occasionally.
"Alfonzo has a lot stronger arm and has been hitting well," said Alou, while Greene -- battling a chronic sore right shoulder -- is .174 in his last 16 contests.
Cain (8-8, 4.62) is 7-3 with a 3.57 ERA over his last 15 outings, including 14 starts, and he hopes his good streak continues when he faces Los Angeles in a 1:10 p.m. PT game Saturday at Dodger Stadium. He'll oppose right-hander Brad Penny (12-5, 3.43) on FOX.