Updated

Ryan Dempster's scoreless innings streak extended to 33 innings Saturday, and that stretch may continue with another team by the end of the month as trade rumors continue to swirl around the 35- year-old right-hander.

Dempster tossed six shutout innings and became the first Cub to hurl 33 straight scoreless innings since Ken Holtzman in 1969, helping Chicago to a 4-1 win over the Arizona Diamondbacks in the middle installment of a three- game set.

Dempster (5-3) fanned five, scattered four hits and walked three for Chicago, which has won four of its last five contests. The Canadian hasn't given up a run since May 30 and has won five straight starts.

"Like I said before, I am well aware of things going on, rumors and things like that," Dempster said. "But I'm a member of the Chicago Cubs and I'm trying to do my best job for this team."

He threw 89 pitches in his second outing since being sidelined with right lat tightness.

Luis Valbuena registered a pair of hits, an RBI and a run scored, while Reed Johnson and Geovany Soto each racked up two hits apiece.

Joe Saunders (4-6) was charged with four runs -- three earned -- on eight hits for the D-backs, who have dropped eight of their past 11 games. Saunders had been on the disabled list since June 23 with tightness in his left shoulder.

Arizona made things a bit interesting against Carlos Marmol in the top of the ninth after Stephen Drew doubled and Chris Young walked.

But Johnson made a fine catch at the wall in right-center to retire Geoff Blum, and Marmol then induced Jason Kubel into a game-ending 3-6-1 double play to notch his ninth save of the season.

The Cubs tallied a run in the third, a pair in the fourth and another in the sixth to jump out to a 4-0 advantage.

Starlin Castro recorded an RBI single in the third to make it 1-0, while Darwin Barney smacked a run-scoring double and Valbuena added an RBI single to extend to margin to 3-0.

Barney grounded into a double play in the sixth to plate Jeff Baker, who reached on an error, giving the Cubs a 4-0 cushion.

Chris Young belted a solo homer to center in the seventh to account for the final margin.

"We scored two runs in Wrigley Field in two days," D-backs manager Kirk Gibson said. "That's not what we expect to do. We got to do better than that."

Game Notes

Chicago was 5-for-11 with runners in scoring position and left five men on base, while Arizona finished 0-for-5 with RISP and stranded eight...Young's homer was his ninth of the year...Prior to the game, Arizona optioned left- handed pitcher Patrick Corbin to Triple-A Reno.