Celtic eased to victory in a bad tempered Parkhead clash which saw three players sent off.
The home side took the lead in 17 minutes when Barry Elliot nodded home.
Twelve minutes later Gerry Crossley whipped in a right wing cross and Elliot glanced in a header beyond Antti Niemi.
In 75 minutes Healy settled matters with a perfectly struck volley and he doubled his tally three minutes later when he knocked in from close range.
As tempers flared in the final 10 minutes, Celts' Peter McDonald and Gers' Stephen Hughes saw red after a midfield clash. And Billy Gibson quickly followed them as the Ibrox side finished with nine men.