Cubs 4, Diamondbacks 1: Ryan Dempster pushed his scoreless-inning streak to 33 with six blemish-free frames and Darwin Barney doubled in a run as host Chicago picked up its third straight win.

Dempster (5-3), who has been the subject of rampant trade rumors and reportedly had scouts from several teams watching him on Saturday, surrendered four hits and walked three while striking out five. His 33-inning streak is the longest of his career and the best by a Cub since Ken Holtzman did the same in 1969.

Starlin Castro and Luis Valbuena each added an RBI for Chicago, which has won 11 of its last 15 games. The Cubs will be looking for their second straight home sweep on Sunday.

James Russell came on in relief in the seventh and surrendered a solo home run to Chris Young, ending the shutout bid. Shawn Camp worked a scoreless eighth and Carlos Marmol allowed the first two to reach in the ninth before getting a deep flyout and a double play to lock up his ninth save.

Chicago got to Joe Saunders (4-6) in the third, when Valbuena led off with a single and moved up on a sacrifice and a bunt single before scoring on Castro’s RBI groundout. The Cubs piled on two more runs in the fourth on a two-out double by Barney and Valbuena’s single.

Saunders spent nearly a month on the disabled list with a strained left shoulder and was charged with four runs - three earned - on eight hits over six innings in his return.

GAME NOTEBOOK: Dempster has gotten the win in each of his last five starts and leads the majors with a 1.86 ERA. … The Diamondbacks have scored a total of six runs in Saunders’ last five starts, dating back to May 29. Saunders is 1-3 in that span despite a 3.00 ERA. … Arizona LHP Patrick Corbin was optioned to Triple-A Reno to make room for Saunders on the active roster. … Diamondbacks LF Jason Kubel (hamstring) was held out of the starting lineup. He came on as a pinch hitter in the ninth and hit into the game-ending double play.