The Ibrox side simply out-muscled and outplayed a Bhoys team whose indiscipline badly let them down with an incredible nine bookings.
The visitors actually had the better of the opening 20 minutes, but with their first concerted attack the Gers took the lead when Nacho Novo headed home at the back post.
Barry Ferguson reacted first to toe-poke his shot home just before the hour mark and Novo converted a penalty 11 minutes from time to underline Rangers' superiority.
Celtic looked the more dangerous side early on and Scott McDonald's overhead shot was touched away by keeper Allan McGregor at full stretch.
Rangers were restricted to long-range efforts by Charlie Adam, before Novo carelessly gave away possession at the edge of the area to McDonald, but the striker's shot was gathered by McGregor.
The home side took the lead when Ferguson's pass found Alan Hutton whose dangerous curling cross was left by Darren O'Dea and Stephen McManus, allowing Novo to squeeze the ball home at the back post with his head.
The Celtic defenders looked at each other but it was a superb cross by Hutton which led to their confusion.
Novo nearly increased Rangers' lead after a good run by Adam but his shot drifted narrowly over.
There was a three-minute delay just before half-time when McManus was stretchered off after a clash of heads with Daniel Cousin.
After the break Gary Caldwell saw his powerful shot pushed away by McGregor before Rangers doubled their lead.
Hutton's powerful run led to Cousin crossing from the right and, after the ball stuck between Ferguson and John Kennedy, it was the Gers skipper who was quickest to react and shoot past Artur Boruc from ten yards.
Celtic were stunned by this setback and their loss of control led to a spate of needless bookings.
Rangers made sure of the points when Ferguson's pass played Adam into the area and the midfielder enticed Evander Sno into a rash challenge which led to a penalty.
Novo make no mistake with his spot-kick, but there was still time for a final flare-up which led to five bookings once the referee restored order.