Gloucester go third in Premiership with win over Exeter
Ahead of the Autumn Nations Series, Wales wing Rees-Zammit got the hosts off to a flying start after just three minutes.
Santiago Carreras, Santiago Socino, Charlie Chapman, Ruan Ackermann and captain Lewis Ludlow also scored tries for Gloucester to seal a bonus point win.
Exeter stayed in the game for over an hour thanks to tries from Jack Maunder, Ruben van Heerden and Josh Hodge, but slipped to a third defeat in six league games.
The Chiefs remain sixth in the table, reduced to 11 clubs on Friday by Wasps suspension for the rest of the season and subsequent relegation.
Gloucester close to within nine points of leaders Saracens and with a game in hand to come.