Both teams played out an absolute classic football at Kenilworth Road.
Gabriel Martinelli opened the scoring and Gabriel Jesus added a second on half time after Gabriel Osho had equalised with a header from a corner. Kai Havertz scored the sixth goal of a pulsating game before Rice headed in the late winner from a Martin Odegaard cross.
However, the Arsenal goalkeeper was at fault for two of Luton’s goals on the night.
The Gunners had gone 2-1 up before David Raya conceded the two errors.