The Cardinals (3-1, 3-1 Mid-American Conference) built a 24-3 lead after two-and-half quarters before Toledo (2-2, 2-2) rallied.
Jack Knight's 31-yard field goal with 13:06 remaining extended Ball Sate's lead to 18 before Peters led a 56-second drive that resulted in a score when he found Bryce Mitchell from 28 yards out with 5:31 left.
Toledo forced a three-and-out, and in relief of Peters, Carter Bradley threw an 18-yard touchdown to Mitchell with 2:34 remaining.
Peters threw for 363 yards and Winstead caught six passes for 113 yards.
More AP college football: https://apnews.com/Collegefootball and https://twitter.com/AP--Top25
How Kansas plans to go about replacing Miles
Adam Rittenberg describes the details behind Kansas' parting ways with Les Miles and how it will proceed with finding a new head coach.
Ja'Marr Chase ready to bring his skill set to the NFL
Take a look at the highlights from LSU's Ja'Marr Chase as he gets ready to be one of the top receivers off the board in the NFL draft.
The highlights that make Penei Sewell the top O-lineman in the draft
Take a look at the highlights from Oregon OT Penei Sewell as he prepares to be an early pick in the NFL draft.
Trevor Lawrence's college highlights show his NFL readiness
Relive QB Trevor Lawrence's college career at Clemson as he heads into the 2021 NFL draft as the top overall prospect.
Mac Jones' college mixtape: A winner ready for the next level
Check out highlights from Alabama QB Mac Jones' college career ahead of the 2021 NFL draft.
Miles out as Kansas head coach
Scott Van Pelt reads the statements from Les Miles and Kansas AD Jeff Long after the university announces its decision to part ways with Miles.