Dempster, who is coming off a disappointing 10-14 season with a 4.80 ERA, had his first tough outing of spring training in the Cubs split squad's 12-2 loss to the Arizona Diamondbacks.
Dempster gave up three runs in 3 2/3 innings on eight hits, including Henry Blanco's second home run of the spring, with three strikeouts and a walk.
"It was a good work day," Dempster said. "I threw some good pitches, some not so good ones. I have to start executing more pitches more consistently. I'd throw a good one then a bad one. I threw some really good pitches with stuff I am working on and I made a few mistakes."
Diamondbacks right-hander Ian Kennedy, who has had the flu, felt strong in becoming the first Arizona pitcher to go four innings. He gave up five hits, a walk and struck out three.
"I felt like sometimes out of the stretch that I was pulling some pitches, but overall I was pretty happy with it," said Kennedy. "I felt like there were some guys on and I had to battle but I got my outs."
The Diamondbacks' offense finally came to life. They came into the game hitting a Cactus League-low .227 and had five players in the lineup against the Cubs with a sub .200-batting average, but cranked out 16 hits.
"We (swung) the bats good today," Diamondbacks manager Kirk Gibson said. "We were much better. It was good situational hitting."
Wood was pulled with the bases loaded and Josh Beliveau promptly gave up a grand slam to Goldschmidt in the start of seven-run seventh inning to break open a 4-0 game.
"Most of the time those things (a seven-run inning) are a result of not throwing strikes," Cubs manager Dale Sveum said. "Obviously that inning was. When you have to throw a strike to Goldschmidt that's going to happen when the guy has that kind of power and bat speed.
"The bottom line is not being able to keep the ball down in the strike zone," Sveum said.
The Cubs sent 21-year-old right-hander Aaron Kurcz to the Boston Red Sox as a player to be named as part of the compensation for Theo Epstein. Kurcz was selected in the 10th round of the 2010 draft. The Red Sox still owe the Cubs one player to complete the deal.