OSU trailed three times in the first half, but Robinson's 8-yard scoring pass to Hubert Anyiam with just two seconds left in the second quarter led to a 24-17 halftime lead.
Overall, Robinson completed 22-of-35 passes without an interception.
Lucien Antoine scored on a 26-yard second-quarter interception return.
Dan Bailey kicked four field goals.
Keith Toston scored once on 24 carries for 87 yards, and Anyiam finished with 119 yards on 10 catches for the Cowboys (5-1, 2-0), who have won four in a row.
Missouri quarterback Blaine Gabbert completed 22-of-44 for 332 yards and one touchdown but three interceptions.
Danario Alexander made nine receptions for 186 yards, while Derrick Washington added a second-quarter rushing touchdown for the Tigers (4-2, 0-2), who have lost two straight.