Brendan Rodgers had expressed gratitude to his Celtic players even before an Old Firm ball was kicked.

That squad, Rodgers insisted, were worthy of immense praise “irrespective of the result” against their oldest adversaries. “It has been a huge achievement,” added Rodgers of an unbeaten domestic run which has now stretched to 24 matches. Celtic dismissed any suggestion that if this spell of results was to end, Ibrox was the most likely venue; a notion which had been enhanced as Kenny Miller handed Rangers a deserved derby lead.

Celtic’s recovery pretty much summed up their season. The key men in that, Moussa Dembélé and Scott Sinclair, have been central to the raising of standards by Rodgers. Dembélé emphasised why he is amongst the most courted strikers in Europe with a thundering finish before Sinclair, who has seen his career rejuvenated in Glasgow, capped a wonderful performance with the winner. Celtic and Rangers may share a city and famous rivalry but, for now at least, they operate in different footballing stratospheres. With a game in hand, Celtic lead Rangers by 19 points. Legitimate arguments can be made regarding Rangers’ necessity to implement gradual progression after the fiscal chaos of 2012 but history tells us this situation will not be tolerated even in the medium term. Should Aberdeen win their own game in hand, Rangers will slip to third. All the while, the Rangers chairman Dave King, who once issued statements by the thousand word batch, has lost his fondness for publicity. The club does not yet appear altogether stable.

Whilst occasions such as this highlight Celtic’s vast improvement under Rodgers, they also point towards mutual benefit. There is little question that Rodgers has gained on a personal level from his switch to Scotland. The haunted, troubled figure from the closing stages of his tenure at Liverpool is no more; Rodgers’ management star is once again on the rise, to the point where speculation regarding his own future will soon be inevitable.

It is neither fair nor fully explorative to simply point out Celtic’s budget versus the rest of the league. Rodgers has implemented a playing style and attitude that was glaringly lacking under his predecessor, Ronny Deila. He has also kick-started the fortunes of players who once made up the numbers; Stuart Armstrong again performed with distinction at Ibrox, as did Emilio Izaguirre, Celtic’s second-choice left-back. Celtic took a chance on Dembélé and Sinclair where others wouldn’t, a matter which has wider meaning as Rodgers looks to supplement his squad during the transfer window.

“Scottish football is a great place,” Rodgers said. “You experience so much here; great stadiums and great challenges. At Celtic, you get the opportunity to play at the highest level and with great pressure.”

Focus was firmly on Celtic within 12 derby minutes. With Rangers inspired by the attacking promptings of Barrie McKay, early dominance was endorsed by a Miller tap in. The hosts should have doubled their lead, James Tavernier instead failing to pick out Martyn Waghorn with the goal gaping. The cost of that was instantly obvious to anyone with knowledge that Celtic entered the fixture with a record showing an average of more than two goals scored in away fixtures this season.

Celtic found their feet, Dembélé crashing home in the style which illustrated his special talent. Rangers may have been culpable in allowing the France under-21 forward to control a corner kick on his chest but, even then, the standard of finish could not have been anticipated. Moments earlier, Sinclair had been denied by the inside of a post.

Celtic’s Moussa Dembélé celebrates his equaliser. Photograph: Craig Watson/PA

Rodgers hailed his side’s second half display as “outstanding” which owed only a little to typical managerial exaggeration. Dembélé – twice – James Forrest and Sinclair had all been denied before the moment which defined the result. Following intricate play between Armstrong and Patrick Roberts, Sinclair stole in at the back post to provide merely his latest marquee Celtic moment.

Even then, and curiously given the flow of the game, Rangers were never without hope. Miller should have restored parity but struck a post. There ended a proud Rangers run which showed them as unbeaten on league business at Ibrox since Mark Warburton took office a 18 months ago.

“We came out of the blocks so fast but we had to get that second goal at that point,” acknowledged the Rangers manager, fairly. “It is about fine margins. You have to take your chances when they come along.”

Warburton claimed he was “not worried” about the points gulf that exists at the top of the league. Rodgers has no cause to care about it either; he is presiding over a procession.