CELTIC showed plenty of qualities in this long demonstration of cruel supremacy at Celtic Park, but mercy was not one of them.

There could not have been many among the 60,000 present who genuinely believed that this was the last ever Old Firm game yet, even so, Celtic acted like a team determined to unplug the life support machine as Rangers played like a side at death's door. It was a prolonged exercise in unhindered gloating and celebration for the home support and one of grim endurance for the visitors.

No end of doubt and uncertainties hang over Rangers but one matter was cleared up here. Celtic's credentials as champions were proved long ago yet their losing record in the derbies this season had been a source of pleasure for Rangers. The campaign will finish with each club having two home wins yet this, the last of them, will stand as testimony to Celtic's superiority.

Given the unforgiving quality of Celtic's finishing and the verve of their overall play, Rangers would have had to dig deep to live with them. They couldn't, so the match became an unsentimental beating. Charlie Mulgrew and Kris Commons scored to have Celtic coasting before half-time and Gary Hooper lashed home a ferocious third to finish things. It was an uncontroversial and generally unremarkable derby but all of its best players – Commons, Hooper, Mulgrew, Emilio Izaguirre, Joe Ledley, Scott Brown – were wearing green and white.

Celtic set up with three defenders and two wing-backs, allowing Izaguirre and Adam Matthews to bomb down the wings. In Commons they had a jack-in-the-box who was back to the exhilarating form he showed in his early months at the club. He played in the hole behind Hooper and Georgios Samaras and although Rhys McCabe started the match well for Rangers – the 19-year-old won one thumping challenge with Brown – he was unable to cope with Commons. Neither could anyone else for that matter.

Maurice Edu, Andrew Little, Kyle Bartley and Lee Wallace all struggled and lost their individual battles in what was a Rangers horror show. They were exposed and vulnerable where they expected to be reliable: in defending set-pieces. Corners consistently troubled them and the ease with which Celtic scored their first goal will doubtless result in a Murray Park inquiry today. Commons' delivery flew over the scrum of bodies in the box to meet the forehead of the onrushing Mulgrew. Celtic's tallest outfield player, a central defender who is decent in the air, was given an entirely free run to race into the penalty area and connect with a diving downward header which reared up to fly past Allan McGregor.

After the match, Neil Lennon said he had suspected that Rangers were vulnerable at the back post if all their best aerial players could be sucked towards the ball at a cross. The tone of a game can be set by such insights and the Celtic manager will feel that he got one over on Ally McCoist by noticing a flaw in his Rangers team and exploiting it successfully.

A display by Celtic fans had turned one corner of Parkhead into a mock graveyard for Rangers complete with an enormous four horsemen of the apocalypse banner – the four shown as Lennon, the taxman, the Grim Reaper and Craig Whyte – and other banners of headstones with derogatory messages. There wasn't much Rangers could come back with against that, and their hopes of being able to spoil some of Celtic's fun on the park had all but gone after just over half an hour. McCoist had an experienced, battle-hardened side but it never looked like one with goals in it and when they soon fell two behind the contest looked done and dusted.

Commons has been a dormant presence for much of Celtic's season but his technique and nerve at their second goal was exquisite. Hooper turned Dorin Goian near the touchline and passed low and hard to Commons. Bartley came flying across like a fire engine going to the wrong blaze and Commons' brilliant first touch instantly took out Rangers' defence and put him clean through on McGregor. He showed class again to clip into the net.

Rangers were a mess by then. They lost 50-50s, gave the ball away, the decision-making was poor and they could have played all day without scoring a goal. Fraser Forster had only two saves to make, an early one from Little and another near the end from Sone Aluko's free-kick.

The remainder of their day was about hanging on. They needed McGregor to keep out a couple of Victor Wanyama efforts and, impressively, a dipping volley from Ledley. There wasn't anything the goalkeeper could do when Commons dispossessed McCabe and the ball was fed via Samaras to Hooper, who evaded Carlos Bocanegra and lashed home.

Tackles by Wallace, Bartley and Brown brought the game's only bookings and the latter sparked a melee as players reacted to his foul on Salim Kerkar. Generally Rangers didn't let their frustrations bubble over. They'll hope to survive to contest another Old Firm game soon, but they couldn't get out of Parkhead quickly enough after this one.