The Brazilian light-heavyweight was dominant from the outset and gained a takedown early in the first round.
Rampage got back to his feet but was hurt by a stinging left hook just before round one came to a close.
Glover continued to push the pace and forced Rampage against the cage in round two, using a mix of single-leg takedowns and bruising body shots to stay ahead.
In round three Rampage looked disheartened but tried to apply pressure without landing any damaging strikes.
Teixeira picked up a wide 30-27 30-27 29-28 win on the scorecards to hand the dangerous Brazilian his 18th straight victory.