The Boilermakers struck first when McCartney drilled a 31-yard field goal, the final play of a 12-play, 78-yard drive.
Illinois tied things up at three when a seven-play, 39-yard drive ended after Taylor Zalewski made a 54-yard field goal.
Purdue broke the 3-3 standoff when McCartney kicked a 29-yard field goal to polish off an 11-play, 62-yard scoring drive.
The Boilermakers will have possession to start the second half.
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