Phil Blatcher rushed for a career-high 247 yards and scored two touchdowns yesterday as 19th-ranked Iowa defeated Michigan State, 36-7, and won its first trip to the Rose Bowl in 23 years.

The Iowa victory, coupled with Ohio State's 14-9 defeat of Michigan, made the Hawkeyes and Buckeyes cochampions of the Big Ten. Both are 6-2 in the conference and 8-3 overall. Michigan State is 4-5 and 5-6.

Iowa, which had 19 straight nonwinning seasons before this year, becomes the Big Ten's representative in the Rose Bowl because Ohio State had been there more recently, going two years ago. Iowa last played in the Rose Bowl in 1959.

Hundreds of Iowa fans ran onto the field after the game, surrounded the Hawkeye players and tore down both goal posts. After Iowa scored its 36th point, several dozen fans ran into the end zone and attempted to do 36 push-ups each.

In an interview last week, President Reagan recalled his career as a sports announcer and said he became an Iowa fan in the first game he broadcast. When reminded Iowa had a chance to go to the Rose Bowl, Reagan replied: "I suppose generally now I'm supposed to be totally neutral, but I can have some warm memories, can't I?"