The Scottish Premiership champions looked second best throughout the game as Steven Gerrard's side won back-to-back games at Ibrox against their bitter rivals.
James Tavernier opened the scoring inside the first two minutes when his free-kick deceived Scott Bain in between the sticks before Arfield doubled his sides lead in the second half.
Speaking to Sky Sports Football after the match, Arfield praised his team for the win and explained how important their midfield battle with the Bhoys was.
On enjoying his midfield battle with Brown: "I always do," Arfield told Sky Sports Football. "It's not just one player, it's not just him. It was all about us today. We knew if we win that battle [in midfield], which we did, we'd win the game."
Rangers have now won six games on the bounce in the Premiership and they will be hoping these recent performances is a marker for their title charge next term.
Celtic, who are yet to appoint a full-time manager for next season, have won eight Premiership titles in a row and will be well aware of the threat facing them from their rivals.
What happens in the summer, in terms of Rangers summer recruitment, Celtic's new manager and summer transfers, will lay the foundations as to who will be the top team for the next campaign.
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