He capped his lone drive by firing the ball into the chest of receiver Stefon Diggs, who beat Isaac Yiadom on a one-yard quick slant for a touchdown.
"I think it was a great first drive. It was a great start to the preseason," said Cousins, who signed a three-year, $84 million deal in the offseason.
Cousins, who played the past two seasons for the Washington Redskins on a franchise tag, topped the 4,000-yard mark for the third straight year in 2017. He finished with 4,093 yards, with 27 touchdowns and 13 interceptions.
Keenum struggled in his first outing on Saturday, completing just 1 of 4 passes for five yards.
"It's just frustrating not playing well and you don't have a chance to bounce back from it," Keenum said.
Keenum started 14 regular-season contests and both postseason games last season while leading the Vikings within one win of the Super Bowl. The former journeyman made $2 million on a one-year deal in 2017 before signing a two-year, $36 million contract with Denver in the offseason.