The first-place Cubs built a 6-0 lead, then permitted four runs during a soggy eighth inning and endured a rain delay of 1 hour, 44 minutes before sealing their fourth straight win.
"It's good we scored enough runs. That's what you call a hold-on victory, but it's still a victory," Chicago manager Dusty Baker said.
Before the game, the Cubs spoke about the need to rally together during the absence of Sosa, who began a seven-game suspension for using a corked bat.
Chicago then received a contribution from virtually everyone in the lineup. Seven players scored runs, and five had at least one RBI.
Alou had two hits, including the 1,500th of his career, and drove in two runs as the Cubs moved nine games over .500 (36-27) for the first time since the end of the 2001 season.
"In a perfect world, we'd like to have Sammy here," Clement said. "But we don't, so we have to go about our business and keep working hard."
Clement (4-6) gave up two runs, struck out six and walked two. He has won two straight starts after going six in a row without a victory.
Joe Borowski got the final four outs for his 12th save.
The victory brought a satisfying end to a difficult day for the Cubs, who learned shortly after noon about Sosa's suspension for using a corked bat in a game June 3.
Sosa took batting practice, thrilling the early arriving fans with several titanic drives. But he cannot play in a game again until June 18.
Chicago, which went 10-7 earlier this season while Sosa was on the disabled list, again fared well without him.
Held hitless through three innings by Omar Daal (4-7), the Cubs took a 3-0 lead in the fourth. After Alex Gonzalez reached on an error, Alou hit an RBI double, Eric Karros walked and Damian Miller doubled in two runs.
Baltimore ended a run of 14 straight scoreless innings against the Cubs in the bottom half. With two on and two out, Jay Gibbons was credited with a double when Kelton misjudged his opposite-field liner to left and allowed the ball to glance off his glove.
Kelton, who earlier got his first hit in the majors, made it 7-2 with an RBI single in the eighth.
As the rain slowly increased in volume, the Orioles scored four in their half. Batista hit a two-run single, Surhoff singled in a run and Luis Matos drove in a run with a grounder before Borowski struck out Geronimo Gil.
That's when the umpires called for the tarp.
"We had something going, and then it rained," Orioles manager Mike Hargrove said. "At least we fought back and made a game of it."
Matos had his 15-game hitting streak snapped. It was the 50th career victory for Clement (50-56). Chicago improved to 6-2 in interleague play; the Orioles are 1-7.