On his first start since the beginning of March after a metatarsal injury, the Australia international midfielder opened the scoring with a delightful diving header in the 14th minute.

It was classic Cahill and in the 50th minute his outstanding pass helped to orchestrate Leon Osman’s brilliant clincher from 22 yards.

A 65th-minute strike from Cleyton Alexandre Silva had home nerves jangling but substitute Victor Anichebe ensured Everton rounded off proceedings with a superb late third.

And with Thomas Gravesen also making a return to action after injury, Everton followers left Goodison Park encouraged their side can make a serious impression in the competition this season.

Blues boss David Moyes, still seething from Saturday’s controversial Merseyside derby, made five changes to the side which lost 2-1 at home to Liverpool.

Larissa, meanwhile, included former Everton striker Ibrahima Bakayoko in their starting line-up.

The Ivory Coast striker first arrived on Merseyside in October 1998 for £4.5million from Montpellier but after failing to adjust to the English game he joined Olympique Marseille the following summer.

The visitors should have taken a ninth-minute lead when Cleyton sidefooted weakly wide.

Moments later the imposing Bakayoko fleetingly threatened with a menacing run and shot from 18 yards which drew a vital block from Leighton Baines.

After the early scare, Everton drew first blood in the 14th minute.

Osman and Mikel Arteta worked a quick one-two from a corner on the left and Osman’s whipped cross was greeted with a diving header from Cahill which flew into the back of the net.

The manner in which Cahill celebrated his goal said everything about his bitterly frustrating spell on the sidelines.

While Everton were busy qualifying for a UEFA Cup spot towards the end of last season, Cahill was forced to watch from the stands.

He originally sustained the injury at Sheffield United on March 3 and then aggravated it in a friendly against Werder Bremen at the end of July.

Indeed, Cahill’s only senior action in the past six months had been for his country in the summer’s Asia Cup.

But his impressive display confirmed he has lost none of his predatory instincts in front of goal.

It should have been 2-0 in the 21st minute after more good work from Cahill.

Neat footwork from Steven Pienaar down the right flank allowed the South African to find Cahill with a short pass deep in Larissa territory.

The former Millwall man could have shot but opted to pass to James McFadden, but his scuffed effort was easily collected by visiting goalkeeper Stefanos Kotsolis.

Joleon Lescott then accidentally clashed heads with Bakayoko moments later and found himself in the referee’s notebook on the half hour after a foul on Georgios Gkalitsios.

With McFadden left to plough a lone furrow in attack, Everton had little physical presence in attack but Arteta, Osman and Cahill offered plenty attacking impetus.

In the 39th minute a deep free-kick from Arteta was volleyed wide by Lescott at the far post and seconds later Cahill fired goalwards from 20 yards with a shot which Kotsolis turned away for a corner.

Everton needed just five minutes of the second half to extend their advantage thanks to Osman’s brilliant effort.

The architect of the goal was Cahill, whose outstanding pass sent Baines clear down the left flank.

He whipped in a low cross which Pienaar audaciously flicked into the path of Osman – who slammed the ball into the top corner from 22 yards.

The Greeks pulled a goal back in the 65th minute after Lescott was dispossessed inside his own 18-yard box by Cleyton.

The striker showed admirable pace to glide past the England defender, then Joseph Yobo, before striking a low shot past Tim Howard.

That set the tone for a period of sustained Larissa pressure but Anichebe eased home fears in the 85th minute with a superb run and shot from inside the visiting penalty area to seal an ultimately comfortable win.