Celtic's returning hero Shaun Maloney won the man-of-the-match award against Falkirk after an 18-month absence then pinpointed team-mate Aiden McGeady as a star Parkhead player.
Maloney left for Aston Villa in January 2007 but became a Hoops player for the second time on Friday after manager Gordon Strachan ended his miserable time in the Midlands by handing him a four-year deal.
The 25-year-old came on as a first-half substitute for Jan Vennegoor of Hesselink at Celtic Park on Saturday after the Dutchman was left crumpled in a tackle by Bairns defender Lee Bullen.
Almost instantly the Scotland player made an impact, winning a free-kick from which Stephen McManus bundled home his 31st-minute opener.
Maloney set up Georgios Samaras for an easy second goal which effectively clinched the points before the interval.
Strachan's side turned on the style after the break, with McGeady and Shunsuke Nakamura vying with Maloney for the top billing but it was the former Villa player who cleverly set up Samaras for the Greece international striker's second goal.
But Maloney, who often kept a younger McGeady out of the side during his first spell at Celtic Park, praised the Republic of Ireland wide man for the improvements made in his game over the last year and a half.
He said: "I knew how good Aiden was when I left but he has improved a hell of a lot. He has pretty much everything now, the final delivery, the shot or pass, he has that end product to his game now. And he scares the life out of defenders when he starts running at them."
Maloney's return to Parkhead may have come at a vital time as Strachan could be without his first-choice strike force for next week's Old Firm game.
Scott McDonald missed the visit of the Bairns with an abductor injury and Jan Vennegoor of Hesselink's injury will be assessed over the weekend.
Falkirk manager John Hughes was unhappy at conceding the first goal, claiming McManus had handled Nakamura's free-kick on its way into the net.
Hughes, whose side have lost their opening three SPL games, tried not to be too downbeat: "I will take the positives out of it. One or two of our young players got a taste of it and sometimes to blood one or two you have to take a hit."