The Hoops striker opened the scoring in the 12th minute with a trademark poacher's goal before Raith skipper Allan Walker levelled in the 27th minute with a deflected shot from 20 yards.
However, Hooper minimised any chances of a cup upset when he restored Celtic's lead before the break before completing his scoring spree in the second half against the Irn-Bru First Division side who were valiant but out of their depth.
With bigger tasks ahead in the coming weeks, especially in the Champions League, Celtic manager Neil Lennon would have been glad to see midfielders Beram Kayal and Joe Ledley get some game time following their lengthy absences out with ankle and groin complaints respectively.
Kayal recovered from the injury sustained in the 2-0 Champions League play-off win away to Helsingborg in August and his inclusion was one of six changes to the side which beat Dundee 2-0 in the Clydesdale Bank Premier League on Saturday.
New signing Efe Ambrose made his first start for the Hoops in midfield, with goalkeeper Lukasz Zaluska together with Thomas Rogne, Dylan McGeouch and Tony Watt coming in against a Rovers side which had Grant Anderson in for David Smith.
The fixture did not capture the imagination of the home fans and the top tier of Celtic Park was closed, with most of the noise in the low-key early stages coming from the travelling supporters, encouraged by their side's efforts to pass the ball.
However, it was their desire to play football which saw the underdogs come unstuck.
Defender Jason Thomson's pass from wide on the right touchline was cut out by James Forrest who sped forward and switched the ball to McGeouch whose low driven cross was steered in almost casually from close range by Hooper.
It looked like it would be an early surrender by the visitors.
In the 14th minute Rovers goalkeeper David McGurn made a fine save from McGeouch's right-footed drive from 12 yards after he had been set up by Hooper.
Seconds later, the former Scunthorpe striker had a shot well saved by the Kirkcaldy number one in the same spell of pressure which ended with Rogne smashing the ball off the post.
The tempo then dropped as it appeared Celtic had everything in hand.
Watt flashed a shot over the bar from the edge of the box in the 25th minute but two minutes later the visitors, somewhat out of the blue, had their vociferous band of fans in raptures.
There was still plenty to do when striker Brian Graham played the ball into the unmarked Walker 20 yards from goal but his drive took a nick off Hoops defender Kelvin Wilson before spinning over Zaluska and going in off the post.
The mood inside Celtic Park changed immediately and the home fans groaned in the 33rd minute when Kayal scooped a Charlie Mulgrew corner over the bar from a few yards out.
However, order was restored in the 37th minute when Forrest raced down the left and his cross into the middle was, again, confidently converted by the unmarked Hooper.
Celtic's rearguard were prone to the occasional lapse and Raith should have levelled for the second time in the 50th minute when Walker set up Brian Graham with a fine cross but the big striker did not get enough on his header from eight yards and the ball went wide.
That was effectively the last hope Rovers had of pulling off a shock.
Hooper grabbed his hat-trick in the 58th minute when he finished off a fine move involving McGeouch and Adam Matthews by drilling an angled shot past McGurn and in at the far post.
On the hour mark the Englishman made it 4-1 when he tapped in from almost on the line after Kayal's shot lacked the power to see him on the scoresheet.
Kayal then made way for Ledley, who also returned for the first time since the win in Helsingborg, and watched in admiration, as did most inside Celtic Park, when Forrest hit the post in the 77th minute with a curling shot from outside the box.
McGurn was called into action again when he had to tip a powerful long-range drive from Matthews over the bar and thereafter it was simply a matter of Rovers keeping Celtic at bay.
- Celtic Park