DeHaan, who took just four shots and scored six points in Friday's loss to Minnesota, was much more aggressive in going 8-for-21 from the field for the Spartans (9-5, 1-1 Big Ten).
Keane was 7-for-21 from the field and had a strong drive to the basket and two free throws to keep the Buckeyes (9-3, 0-1) at bay.
Michigan State coach Suzy Merchant had her blonde hair spray-painted green at center court by her players after the upset. Her team bounced back from its recent anemic rebounding to rule the boards 44-35.
Star Allen had 12 points, Marcella Packer and Jantel Lavender 11 each, and Ashlee Trebilcock 10 for Ohio State, the preseason conference favorite. Allen added nine rebounds and five assists.
The Spartans led 34-29 at the half and built their lead to 13 points several times in the second half.
It was the first win over a ranked team in three tries for Merchant as the Spartans' first-year leader.
Michigan State grabbed 22 offensive rebounds, 15 more than they managed against Minnesota, and had 12 steals. Freshman point guard Brittney Thomas had five offensive boards and five steals. She also committed 11 turnovers.
The Spartans had chances to blow the game open but were 2-for-15 from 3-point range. They won in a way that few expected, with a 15-4 edge in second-chance points.
The Buckeyes outshot Michigan State from the field 39.3 percent to 35.8 percent, but had just 11 assists to go with 20 turnovers. Those mistakes kept Ohio State from getting closer than five in the late stages.
Packer had six turnovers and only one assist for the Buckeyes, who lost for just the third time in their last 35 league games.