Morton, the Pirates' No. 4 starter, allowed just a single to Jimmy Rollins. The Phillies' only other hit came against Pirates closer Joel Hanrahan.
"He pitched well all spring and today he was very efficient," Pirates manager Clint Hurdle said. "The breaking ball was there."
Alvarez connected off Cole Hamels for his second home run this spring. The Phillies' lefty gave up four hits in three innings.
"He's hit everywhere he's been," Hurdle said. "He has fielded exceptionally well and the swing is going to be there. We just want to see more consistency."
After the game, the Phillies finalized their Opening Day roster, purchasing the contract of Pete Orr and, reassigning infielder Delwyn Young and catcher Erik Kratz to the minor leagues.
The Phillies, who went to the World Series in 2008 and 2009, came up short in the NLCS last season. In response, they traded to bring back pitcher Cliff Lee, who led them to the NL pennant in 2009.
He'll team with Roy Halladay in what is proabably the game's best rotation.
"I think we're all anxious, more so to get back to the postseason," said Halladay, who will start Friday against the Astros. "Opening day is just the start of it. Crazy things happen in baseball. It obviously takes a lot, and just because you have certain names on paper, it doesn't guarantee you anything."
The Phillies also placed second baseman Chase Utley and closer Brad Lidge on the 15-day disabled list, along with infielder Brian Bocock, outfielder Domonic Brown and pitcher Brian Schlitter.
"If we all go out and do our jobs the way we're supposed to and are able to stay healthy, we like our chances," Halladay said. "But I don't think any teams are going to go running from us just because of the guys that we have on our roster."
Notes: Pittsburgh traded minor-league INF Jim Negrych to the Marlins for RHP Carlos Paulino. ... The Pirates also optioned RHP Chris Leroux to the minors.