Zach Zwinak added 135 rushing yards, but the Nittany Lions (7-4, 5-2 Big Ten) did most of their damage through the air against the porous Hoosiers (4-7, 2-5).
Indiana did turn two turnovers into 10 points, including a 46-yarder from Mitch Ewald to get within 28-22 in the third quarter.
Zwinak rumbled in from 1 yard out on the ensuing drive to put Penn State back ahead comfortably by two touchdowns.
Cameron Coffman threw for 454 yards for Indiana. With just a trip to Purdue left on the schedule, the Hoosiers lost a chance to become bowl eligible with six wins.
Penn State star linebacker Michael Mauti was carted off in the first quarter after hurting his left knee.
The emotional heart of the Penn State defense, Mauti was having a standout season before getting hurt while being blocked after appearing to get hit low by another Hoosier, running back D'Angelo Roberts.
A silent crowd rose to its feet and then applauded Mauti in unison as he was taken to the locker room, his hands on the front of his helmet. Injuries -- one to each knee -- already cut short two seasons for Mauti earlier in his career.
The offense gave Penn State fans something to smile about on a record-setting day for both McGloin and Robinson, who took advantage of an overwhelmed and poor-tackling Indiana secondary.
McGloin finished with a career-high 395 yards on 22-of-32 passing with an interception, and eclipsed Daryll Clark's single-season passing record of 3,003 yards.
Robinson, a smooth sophomore, set the school single-season reception mark with 73 after burning the Hoosiers on the afternoon for 10 catches for 197 yards, also a career high.
He's become a master of making mid-air adjustments for spectacular catches.
One score from 26 yards out came after jumping high and reaching across his body over cornerback Brian Williams in the end zone; the third touchdown catch was on a one-handed grab in the air from 10 yards with another defensive back draped over him.
Those scores sandwiched a 53-yard catch-and-run for a TD after Robinson twisted out of a tackle and pulled away from the gassed secondary.
The success of McGloin and Robinson is testament to job first-year coach Bill O'Brien has done in reviving a Penn State offense that had struggled in the previous two seasons under the late coach Joe Paterno.
In this new era of Penn State football, the high-octane offense has just as much fun as the defense.
With Mauti out, the other half of O'Brien's outstanding outside linebacker duo took charge with Gerald Hodges registering 12 tackles and an athletic interception. Several plays after leaving briefly for a cramp, Hodges leaped to block Coffman's pass at the line of scrimmage then stumbled forward and caught the ball before it hit the ground.
McGloin connected with Zwinak for a 16-yard touchdown pass on the ensuing drive.
Indiana did cut a 15-point halftime lead to six with 8:34 left in the third quarter after Stephon Houston turned a screen pass into a 79-yard touchdown reception -- Ewald missed the extra-point attempt -- and Ewald's 46-yard field goal. Penn State fans wondered if season-long woes in the third quarter would haunt their team on the way to a big upset.
It wasn't to be.
Zwinak and Michael Zordich answered with rushing touchdowns in the third quarter, and cornerback Adrian Amos intercepted Coffman on fourth-and-2 at the Penn State 17 early in the fourth to ensure the Hoosiers finished the season with a losing record.
Penn State is guaranteed to finish the season with a winning record -- something few prognosticators thought could happen after about 10 players left the program following offseason NCAA sanctions for the Jerry Sandusky child sex abuse scandal.
Mauti and Zordich helped keep most of the team together, though, after making impassioned statements they were sticking with O'Brien two days after the sanctions were announced in July.
Coffman was 33-of-59 passing for two picks to go with his two touchdown passes. Shane Wynn had 12 catches for 108 yards.