Marshall made the score 42-28 when Jermaine Kelson returned a blocked punt for a touchdown.
Purdue added to its advantage when Paul Griggs kicked a 33-yard field goal, capping off a 15-play, 62-yard drive to give the Boilermakers the lead, 45-28.
Caleb TerBush clinched a 200-yard passing game with 78 in the quarter, part of his 260-yard day through three quarters for Purdue.
The Thundering Herd have the ball at their own 44-yard line to begin the fourth quarter.
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