Instead, he had the shortest outing of his 266 career starts.
"We have a lot of work to do in the next five days, that's for sure," manager Mike Quade said.
Dempster allowed seven runs on four hits, four walks and a hit batter — all in the first inning. He needed 40 pitches to record only one out as the Arizona Diamondbacks routed the Cubs 11-2.
"That was not how I drew it up," Dempster said. "Thank God the month of April for me is over with."
Dempster (1-3) watched his ERA balloon from 7.63 to 9.58 in the span of 35 minutes.
"I lacked execution today," he said. "I put us in a huge hole and I was unable to make pitches when I needed to make them. There's really not much more than that. I could look at it 80 different ways if I wanted to but it just came down to not making the pitches I needed to make."
Dempster's struggles epitomized the difficulties all of Chicago's starters have had. The Cubs' rotation entered 5-10 with a major league-worst 5.91 ERA, numbers that got considerably worse on Thursday.
"We need him to pitch better, especially given the situation we're in," said Quade, whose club has lost four straight and six of seven. "We are counting on him heavily for the entire season, let alone what we're going through right now."
Stephen Drew hit his first career grand slam off Dempster to spark Arizona's seven-run first inning, a franchise record.
Drew finished with a career-best five RBIs and Miguel Montero also homered and drove in three runs. Barry Enright (1-2) earned his first win since Sept. 1 for the Diamondbacks, who have won three of four.
"We kept pushing," Arizona manager Kirk Gibson said. "That game could have tightened up very quickly."
Enright, who had been 0-7 with a 7.40 ERA in nine starts since his previous victory, allowed one run and three hits in the first six innings before tiring in the seventh. He gave up two runs, five hits and four walks. He struck out four in a season-high 6 2-3 innings.
"It's been a while since my last W," Enright said. "I'm glad I'm out of April now. It's hard. It's definitely hard when you lose a few in a row."
Enright also hit a looping RBI single to right for his first hit of the year, and Chris Young added a two-run single to left in the first. Arizona sent 12 batters to the plate in the inning against Dempster and reliever Justin Berg.
"It was a cheap hit," Enright said.
The seven runs were the most for the Diamondbacks in any inning this season and topped by one the franchise mark of six first-inning runs accomplished seven times, most recently on Aug. 28 against San Francisco.
Arizona had scored nine first-inning runs in its first 23 games combined.
Montero hit an RBI double to left in the second and homered to right in the third against Berg to give the Diamondbacks a 10-1 lead.
Drew drove in Young with an RBI groundout in the seventh to make it 11-2.
Josh Collmenter allowed only a walk in 2 1-3 innings in relief of Enright.
NOTES: Arizona drew a season-high nine walks. ... Dempster failed to get out of the first inning only once before, recording just two outs on Oct. 5, 2001, for Florida against Atlanta. ... Dempster is 2-8 with a 6.72 ERA in 19 career appearances and 15 starts against Arizona. ... Drew's grand slam was the 46th in Diamondbacks history and the first since Sept. 1, when Brandon Allen hit one against San Diego. ... Young became the 23rd Diamondbacks player to have two hits in the first inning. ... Arizona third base coach Matt Williams made his season debut in the coaching box after missing nearly a month because of a broken foot.