The Crimson (4-0, 2-0 Ivy League) outgained Cornell (0-4, 0-2) 499 total yards to 192 and converted one of three interceptions and a fumble into scores.
Hosch was 14 of 30 for 244 yards, with TD strikes of 47 yards to Ben Braunecker, 19 yards to Anthony Firkser and 46 yards to Justice Shelton-Mosely. Hosch also scored on a 3-yard run in the fourth quarter.
Paul Stanton Jr. gained 101 yards on 17 carries and scored on a 2-yard run.
The victory is Harvard's 13th consecutive Ivy League win and 10h straight win over Cornell dating back to 2006.