Stoke manager Tony Pulis was also able to bring in a couple of additions with new signings Ibrahima Sonko and Danny Higginbotham – returning for a second spell at the club – coming into the side.

In a cagey first half, shots on goal were a scarcity at either end but it wasn’t long before what has already become Stoke’s trademark weapon of Rory Delap’s long throw-in began to rear its ugly head.

That’s not to sneer at what he does though. It’s not pretty and many would say it’s crude – especially at this level – but Merseyside fans will realise just how effective it is from Dave Challinor’s days at Tranmere when ballboys armed with towels and gaps in advertising boards provided assistance.

Everton managed to weather the storm of Delap’s canons in the first half and after falling victim to some clinical finishing by Portsmouth a fortnight earlier, they took the lead with their first effort on the Stoke goal four minutes before the interval.

In a move started by a towering Fellaini header, Mikel Arteta threaded the ball through to Cahill, who laid off to Yakubu with the Nigerian taking a touch to beat Sonko before dispatching a cool left-foot finish past Sorensen from the edge of the area.

When Everton doubled their advantage just six minutes after the restart it looked like established Premier League class was going to prove enough for Moyes’s men to cruise to a second away success of the fledgling campaign.

Arteta’s inswinging free-kick from the right-hand side was nodded in by a glancing header by Anichebe, who had his back to goal when making contact, registering in the Premier League for the first time in 13 months

However, playing sides fresh from a successful year coming up from the Championship in the early weeks before the confidence gets worn down by defeats and injuries often provides a stern test as Everton no doubt considered when handed West Brom, Stoke and Hull in succession for the first three away days.

Buoyed by a fortunate deflection, Pulis’s men ensured it was game on by pulling a goal back just four minutes after Everton’s second.

Goalkeeper Tim Howard looked to have cleared the danger from a Delap throw but his punch out deflected off Cahill to Seyi Olofinjana and the Nigerian midfielder netted with a perfectly-struck volley.

With the visitors still rocking, Ricardo Fuller thought he’d equalised when he rounded Howard before placing the ball into an empty net but play had already been stopped for his earlier challenge from behind on Joseph Yobo and Everton were annoyed they were unable to take their free-kick early as the home players celebrated their ‘goal’ by the corner flag among the pandemonium.

They did draw level soon after on 63 minutes though when Jagielka replicated Anichebe’s glancing header – only this was from another long throw-in by Delap and was directed into his own net.

It seems the best way to defend Stoke’s most potent weapon is to leave the ball. In the first half the home fans ‘ooh’ed and ‘ahh’ed when one Delap throw went close, landing on the roof of the net, but if nobody touches the ball it’s not a goal as the laws of the game state you can not score directly from a throw-in.

The game could have slipped away from Everton after referee Alan Wiley went back on his decision to award them a spot-kick following a handball by Leon Cort but after consulting with his linesman, he awarded a free-kick on the edge of the area.

An irate Moyes let his feeling be known to the fourth official and was duly sent to the stands.

The Scot actually only moved a few rows further back, sitting amongst the Stoke supporters – although he was quickly surrounded by several stewards.

But rather than crack in adversity, Everton showed their resolve to hit back with a winner from Cahill 13 minutes from the end as the Australian headed in a left-wing corner-kick from Arteta.

The contest was far from over though and the visitors had to see out some sustained pressure during the five minutes of stoppage time with Howard palming away a shot by Higginbotham at the back post from yet another Delap throw.

Despite Stoke being Premier League novices, there won’t be many sides who come away with an easy three points from the Potteries this season so Moyes will have been pleased to receive some sporting congratulatory handshakes from the home fans around him at the final whistle.

A new start for Everton? Maybe. But things aren’t going to get any simpler over the next few weeks.

This was the first of seven games in a gruelling 18-day spell for Moyes’s men in a period which could shape their whole season so early on in the campaign.

There’s another trip to one of the new boys next up in the league and a Merseyside derby too, but first they’ve got to overcome Fellaini’s former team-mates Standard Liege in the UEFA Cup.

Anyone who saw the two-legged tie against Metalist Kharkiv at the same stage last year or the Belgians’ games with Liverpool last month will know it could be far from straightforward.

But at least they haven’t got Fellaini – or a long throw merchant!