Redding tried desperately to claim his maiden Moto2 win, but despite his pace in the Losail track's twisty sections, Espargaro's straightline speed advantage helped keep the title favourite's Pons Kalex ahead.
Takaaki Nakagami had jumped polesitter Espargaro off the line and pulled out an early one-second lead.
Espargaro and Redding left the rest of the field behind in second and third, swapping places on lap four.
Redding hunted down Nakagami and slipped ahead four laps later, with Espargaro following time next past.
Espargaro made his move five laps from the end, drafting past Marc VDS rider Redding into the first corner.
Redding had no intention of letting the Spaniard get away, clinging to his rear for the rest of the race.
The Briton inched alongside at Turn 10 on the final lap, but had to back out of the move to avoid contact.
He rallied one more time to catch Espargaro again, before finally conceding defeat with a small slide into the final corners.
Nakagami claimed his maiden grand prix podium in a lonely third.
Dominique Aegerter slipped to the front of an astonishing 11-bike scrap to claim fourth, inches ahead of Mika Kallio and Julian Simon.
Ricky Cardus will be checked for lumbar and foot injuries after a mid-race crash. It was a tough race for his Forward team, as Mattia Pasini's wild weekend ended when he was taken out by Mike di Meglio.
Inaugural Moto2 champion Toni Elias was only 15th.
2012 Moto3 combatants Sandro Cortese and Danny Kent reprised their spectacular rivalry in the next class up, before Cortese claimed rookie honours in 17th.
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