Soriano smacked a two-run homer in the eighth inning to power the Cubs to their fourth straight win, a 3-2 decision over the St. Louis Cardinals in the first game of a day-night doubleheader.
With the win, the Cubs opened a two-game lead in the National League Central Division over the Milwaukee Brewers. The Cardinals lost their ninth in a row, but Piniella said it's not a two-team race.
"I never discount a Tony La Russa team and a World Championship team," the Cubs' manager said. "Our job was to come in here and win some games and, hopefully, build some distance between them. So far, we've been able to do that."
Trailing, 2-1, in the eighth against Ryan Franklin (4-4), pinch-hitter Cliff Floyd drew a walk to lead off and was lifted for pinch-runner Sam Fuld. Soriano then connected on a 3-2 pitch for his fourth career homer off Franklin. The Cubs' left fielder is batting 7-for-43 on this trip, including four homers.
"I've got the power, but it's more important that I'm seeing the ball good," said Soriano, who has 26 homers this season. "I'm not hitting for average now, but I'm seeing the ball good."
Kerry Wood (1-1) picked up the win, pitching one inning of relief in front of 45,918, the largest crowd of the season at Busch Stadium which included quite a few Cubs fans. It was Wood's first "W" since May 29, 2006.
Dempster, who served up two homers in the ninth in the Cubs' 5-3 win on Friday over the Cardinals, pitched a 1-2-3 ninth for his 27th save. Piniella had talked to the right-hander after Friday's game.
"I said, 'I have all the confidence in the world in you,'" Piniella said. "I told him, '[Friday] wasn't a good day, but tomorrow, in a similar situation, you're back in there.'"
Dempster appreciated the message.
"I think he wanted to let me know, 'You're in there tomorrow if the situation comes up,'" Dempster said. "I was like, 'All right.' He knows me and that I know I'm in there. Any time you have a tough game, it's like giving you that pat on the butt -- 'Everything's fine, go get 'em, no big deal.'"
It was important for Dempster to get back in a game as soon as he could.
"When you have a rough day, you want to pitch the next day," Dempster said. "I wanted to try to do my job and hold onto the win."
Ted Lilly gave the Cubs a chance to do just that. He gave up two runs on four hits -- two in the first and two in the fourth -- and struck out four over six innings. The lefty had beaten the Cardinals, 12-3, on Monday in a makeup game, and this was his fourth quality start in five outings against St. Louis.
"His command was shaky at the beginning, but he managed to go deep in the game," rookie catcher Geovany Soto said of Lilly.
The game didn't start well for Lilly. With two outs in the Cardinals' first, Albert Pujols singled and Ryan Ludwick walked, and both scored on Jim Edmonds' double that right fielder Daryle Ward had a tough time tracking down.
"That ball went everywhere but to me," Ward said.
Cubs pitching coach Larry Rothschild went out to talk to Lilly in the second after Miguel Cairo reached on an error.
"Larry said, 'You're rushing your pitches. You're trying to do too much, so just make your pitch and get an out, and after that, let's go from there,'" Soto said. "That woke him up."
Mark DeRosa walked to lead off the Chicago second against Cardinals starter Braden Looper, reached third on Soto's double and scored on Mike Fontenot's sacrifice fly to make it 2-1.
The Cubs are still riding the momentum from Wednesday's game in Houston, when they survived a ninth-inning threat by the Astros, but held on for a 3-2 win.
"We have had very good moments," Soriano said. "That game [against the Astros] gave us a lot of motivation here. These are very important games. I think everybody's focused on winning."
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.