The scoreline would have been more comprehensive had it not been for former Hoops keeper Robert Douglas.
The 40-year-old Dees number one had a fine match, brilliantly saving a Scott Brown penalty in the 38th minute only to be beaten just before the break when Hooper hammered in from 10 yards.
Wanyama fired in from distance after four minutes of the second-half and when the one-side match was over, the only conclusion available was that Douglas's performance had prevented the scoreline reflecting Celtic's superiority.
It was a welcome win for Neil Lennon.
Celtic had fought out an encouraging goalless draw against Benfica in their Champions League Group G opener on Wednesday night but Lennon was concerned with his side's SPL form, which had seen them drop seven points in the first five games.
Tunisia striker Lassad Nouioui made his first start, partnering Hooper who came back into the side with Miku and Mikael Lustig dropping out through injury.
Celtic dominated the first-half almost totally with Dundee forced to defend valiantly in front of Douglas.
In the sixth minute Charlie Mulgrew's curling free-kick from 25 yards had the Dens Park number one scrambling across his goal but the ball evaded the far post.
Two minutes later Dees full-back Gary Irvine went down in the Celtic box as he tried to go past Parkhead defender Emilio Izaguirre but any penalty claims were drowned out by the home fans who accused the full-back of diving.
Celtic winger James Forrest drove wide with another effort and the onslaught continued but the champions were exposed all too easily in the 16th minute when Ryan Conroy eased past Parkhead stopper Kelvin Wilson down the left and his cut-back had the Parkhead defence in all sorts of trouble.
However, Dundee striker Colin Nish had his effort blocked before John Baird hammered the ball over the bar from 12 yards.
Moments later, at the other end, Lassad went down in the Dundee box under pressure from Kyle Benedictus but referee John Beaton ignored the penalty claims.
As Celtic remained dominant, Lassad had a weak shot saved by Douglas before driving an angled-shot high over the bar after being set up Kris Commons.
The Celtic pressure, at times, was relentless.
In the 26th minute Benedictus was booked for a foul on Wanyama 20 yards from goal and this time Mulgrew's free-kick, after he appeared to win an argument with Commons over who would take it, forced Douglas into a fine save down at his right-hand post.
Douglas made another good save on the half-hour mark, this time from Forrest's drive, after a slip from Matt Lockwood in his own box had gifted possession to Lassad, who then set up the Scotland international.
Celtic were awarded their penalty when Benedictus clumsily tripped Lassad in the box - the visiting defender perhaps lucky not to pick up another card - but while Brown's spot-kick was powerful enough, Douglas stuck up a hand to knock the ball over the bar.
It looked like the teams would go into the interval level but Hooper showed all his predatory instincts when he latched on to a Brown pass and hammered the ball past Douglas, who this time was helpless.
Dundee almost conceded a second goal a minute after the break when Irvine chested the ball back to Douglas only to see it skip past the veteran keeper but it rebounded off the post and the keeper was able to smother.
However, that only delayed the inevitable which came in the 49th minute when Wanyama took an Izaguirre pass and drilled a shot from 25 yards low past Douglas and in off the post.
It became a matter of how many more Celtic would score.
Commons fired an angled-drive past the far post, Forrest drove straight at Douglas after creating space at the edge of the box, before the over-worked keeper made a great finger-tip save from Lassad's point-blank header.
Among all that Hooper had the ball in the net but the linesman's flag was up.
Tony Watt replaced Lassad and Dylan McGeouch came on for Commons to make his first appearance since breaking his jaw in a friendly against Real Madrid in August.
For Dundee, Martin Boyle came on for Milne and Nicky Riley replaced Baird by which time the fans were watching an extended game of attackers versus defenders.
Hooper smashed the ball off the post from 10 yards after being set up by Watt before Douglas saved a Wilson header on the line.
In the 86th minute Nigeria defender Efe Ambrose came on to make his Celtic debut for Brown and the home side remained camped inside the Dundee's half for the rest of the game.