Arsenal were cantering against the Bulgarian champions thanks to sublime first-half goals from Alexis Sanchez and Theo Walcott and a strike straight after the break from Alex Oxlade- Chamberlain before playmaker Ozil joined the party.
As Ludogorets crumbled, his well-taken goals in the 56th, 83rd and 87th minutes helped Arsenal to their biggest Champions League win since a 7-0 thrashing of Slavia Prague in 2007 and sealed their seventh successive win in all competitions.
Arsenal, who have fallen at the last 16 stage six seasons in a row, lead Group A on goal difference from Paris St Germain with both clubs on seven points. Ludogorets and Basel have one and are effectively playing heading for a Europa League berth.
"In the second half we took control of the game completely and could have scored more," manager Arsene Wenger told reporters. "Ozil has got the taste to score goals.
"We want him to be a provider and a scorer and it looks like he has got that balance now."
Sanchez struck after 12 minutes with a majestic lob over Ludogorets keeper Vladislav Stoyanov but until Walcott slammed home his eighth goal in 10 games from 25 yards shortly before halftime it was a surprisingly even game.
Ludogorets, featuring three Brazilians in their starting line-up, cut through Arsenal's defence several times and should have been level through lively winger Wanderson who forced David Ospina into a sharp save before hitting the post.
The second half was a romp as confidence ebbed through an Arsenal side unbeaten since the opening day of the season.
Oxlade-Chamberlain, making his first start for a month, swept in from close range in the 46th minute and 10 minutes later Ozil raced on to Santi Cazorla's long punt and finished coolly past the over-exposed Stoyanov.
With victory in the bag Sanchez and Walcott were both substituted but Ozil stayed on, first converting substitute Lucas Perez's low cross, then burying a volley to become the fifth Arsenal player to score a Champions League hat-trick.
Despite the emphatic nature of Wenger's 100th European win for Arsenal, the Frenchman admitted his side had ridden their luck.
"We maybe eased off a bit early in the first half, we were sometimes in danger and I would like to give credit to (David) Ospina who saved us twice," Wenger said.
It could, however, have been a cricket score by the end.
"The only good thing is that this is not the heaviest defeat in the history of the UEFA Champions League," Stoyanov said.
Arsenal will try to keep the pressure on PSG in the race for top spot when they go to Bulgaria in two weeks time.
(Editing by Ed Osmond)
