The Scarlets last won the Celtic League in 2004 and finished just outside the playoff places last season for the second consecutive year, ending up three points behind Glasgow Warriors.
However they have started the campaign in fine style under new boss Easterby by comfortably seeing off last season's beaten RaboDirect PRO12 finalists in his first game in charge.
And now Easterby believes the Scarlets have got what it takes to finally challenge for the title again.
"We've struggled in recent years against Leinster and Munster but we showed that we can really mix it with them," said Easterby.
"If we were offered that scoreline, seven tries and only a couple for them, before the game then we would definitely have taken it.
"We have to be realistic as well and it's all about building on this performance."
Scott Williams grabbed the Scarlets' first try before Liam Williams added a second just before half-time to make it 14-6 at the break.
The Scarlets then turned the screw after the interval with North and Fenby going over twice each and Kieran Murphy also crossing.
Ian Madigan scored a late consolation try to add to Devin Toner's just after the hour mark, but there were few positives for Joe Schmidt's side.
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