Hagi (right), pictured celebrating with Danilo, put Rangers on course to exorcise their derby demons with a long-range blast early in the first half at Ibrox.
Robin Propper struck after the interval and Danilo wrapped up a first victory against Celtic in seven attempts for Rangers boss Philippe Clement.
The only dark cloud on a memorable day for Rangers was the sight of Celtic midfielder Arne Engels being struck by a missile thrown from the crowd in the closing minutes.
Beaten for the first time in the league this season, champions Celtic still hold an 11-point lead over second-placed Rangers.
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