The Bulldogs (38-15-1) move into the winners bracket in the eight-team field and will face either Campbellsville University or the University of Rio Grande at 3 p.m. Central Time on Friday.
Greene (7-1) gave up one unearned run and three walks while throwing 137 pitches in the victory. The lefthander was very efficient except for a 30-pitch inning in the fifth. He worked around a walk and a single in the fifth and sixth innings and induced a 5-4-3 inning-ending doubleplay to end the seventh after the Bears plated a run.
He retired the final seven batters of the game and 13 of the first 16 of the contest, giving up just three singles through the first four-plus frames.
Cody Strayer (4-6) was the tough-luck loser for the Bears (38-15-1), giving up three runs in the first two innings before shutting down the Bulldogs for the rest of the contest. He walked three and struck out five in eight innings and did not allow a hit from the second until a leadoff infield single by Monson in the sixth.
The Bulldogs jumped out early with two runs in the first after leadoff singles from Cory Urquhart and Chris Hall. Monson then ripped a two-run double down the rightfield line, giving CU the early lead.
Cumberland added another run in the second when Tyler Anderson led off with a double down the leftfield line, went to third on a wild pitch and scored on Richie Seatons single to center.
CU managed just three hits the rest of the game, Monsons infield single in the sixth and another single in the eighth as well as a double from Seaton to start the seventh.
Shawnee State threatened in the fifth when Dustin Bickmeyer walked after an 11-pitch at-bat and Ryan Queener followed with a single, but Todd Queener and Ryan Bice both flied out to end the inning.
In the sixth Cody Spires singled with one out and Calvin Sluberski drew a two-out walk, but Jordan Maier grounded out to end the inning.
The Bears broke through in the seventh after a leadoff walk to Bickmeyer. Todd Queeners slow roller was booted by Josciel Veras at second and Ryan Queened went to third when the ball bounced away. Bice singled to center, plating a run, but Colin Keim bounced into an inning-ending doubleplay with the Bulldogs still leading, 3-1.