Steven Gerrard's men have failed to hit top form in recent weeks, but still enjoy a 21-point lead over their Glasgow rival at the top of the table.
Celtic does have two games in hand and faces Rangers twice more this season.
But the leader looked in no mood to let its advantage go as it extended its perfect record at Ibrox this season.
Rangers dominated the ball but struggled to create opportunities until Jack broke the deadlock with a powerful volley from the edge of the box.
Without suspended strikers Alfredo Morelos and Kemar Roofe, Rangers failed to build on the lead but held out for a 13th home clean sheet in 14 games.
Elsewhere, Aberdeen manager Derek McInnes failed to back up a vote of confidence from the Dons board in an uneventful 0-0 draw at home to St Mirren.
Scotland striker Lawrence Shankland scored twice as Dundee United boosted its hopes of a top-six finish with a 3-0 win over Livingston as both sides were reduced to 10 men.
Motherwell also suffered from an early red card shown to Stephen O'Donnell as it was thrashed 4-1 at home by Hamilton in a Lanarkshire derby.
A first win six games lifted Hamilton off the bottom of the table, above Ross County, whose clash with Hibs was called off because of a frozen pitch.