The Ibrox crowd had little to cheer either side of defender Emmanuel Fernandez's third goal in 10 appearances, 10 minutes before half-time.
But a clean sheet was enough to see Danny Rohl secure his sixth win in eight league games since replacing Russell Martin, who won only one of his seven Premiership matches in charge.
Victory takes Rangers to within nine points of leaders Hearts, who they face on Sunday, and with a game in hand on the Jambos.
Celtic's lead over Rangers is down to three points ahead of their trip to Dundee United on Wednesday.
After losing the League Cup final 3-1 to St. Mirren on Sunday, pressure is already building on new Celtic boss Wilfried Nancy after losing his first three games in charge.
