Gers boss Steven Gerrard had questioned the quality in the Scottish Premiership in the build up to Sunday's clash, but he will have few complaints about the performance of his side against their Glasgow rivals.
Tavernier's wicked cross-shot from a second-minute free-kick set the tone for a fine showing against a Celtic side that celebrated an eighth straight title by beating Aberdeen last time out.
And Arfield finished a well-worked move just after the hour as Rangers chalked up back-to-back home wins over Celtic for the first time since the 2011-12 season.
Celtic were caught cold when Tavernier's whipped free-kick from the left bypassed everyone, including Bhoys keeper Scott Bain, and nestled in the bottom-right corner.
Jermain Defoe then had a stinger palmed away by Bain before seeing penalty claims after a challenge from Kristoffer Ajer waved away by referee Kevin Clancy.
The visitors had offered little but perhaps should have had a man advantage after 51 minutes when Jon Flanagan received only a yellow card for a clear elbow on Scott Brown.
Celtic's misery was compounded when Glen Kamara powered forward and played a pass into Defoe that the striker cleverly dummied to leave Arfield a one-on-one that he clinically rolled past Bain.
Defoe almost added gloss to the scoreline when he looped an effort on to the top of the crossbar having seen his initial shot well saved by Bain and Celtic were denied a late consolation when Wes Foderingham made a fine stop from Oliver Burke's close-range effort.