Australian playmaker Tom Rogic opened the scoring with an excellent right-footed finish from 12 yards, before a poor mistake from Russell Martin allowed Callum McGregor to curl home a second.
Moussa Dembele then won and scored a penalty just after the break, which saw Ross McCrorie receive his marching orders. Celtic were given a second penalty when Jason Holt fouled Patrick Roberts, and Olivier Ntcham tucked it away.
In what was a superb performance and victory for Celtic, Brendan Rodgers' side are now on course to complete a second successive treble under the former Liverpool boss. BBC Sportscene pundit Stewart reacted by criticising Murty on Twitter.
The heavy defeat could have long-term ramifications for Rangers boss Murty, with some pundits claiming that he needed to win at Hampden Park to stand any chance of being given the Gers job beyond the summer.
However, a disappointing loss could signal the start of something new, with chairman Dave King already confirming that the Scottish giants will be looking to make the "best appointment" possible.