Everton v Sheffield United
It took an early scare to trigger Everton's ruthless streak as they cut a dash to overcome the Blades at Goodison Park.
A Carling Cup third round place was assured courtesy of three goals in 12 minutes late in the first half, as David Moyes' men responded impressively to falling behind to a sucker punch from Richard Cresswell midway through the opening period.
Indeed, a cruel observer would suggest Danny Wilson's League One outfit spent more time in the Everton half celebrating their opening goal than they did in the remainder of the game - such was Everton's dominance in the hour of football that followed.
Ironically, it was Cresswell who provided the equaliser - deflecting a Jack Rodwell cross into his own goal as the home side pressurised their visitors in the aftermath of the unexpected opener.
Then came two goals of real quality - the impressive Ross Barkley teeing up Victor Anichebe for a tap-in before Mikel Arteta produced a peach of a right-foot effort from the edge of the box to make it three.
Having turned the screw in emphatic fashion, the Blues should have added more in the second period but the woodwork and some sloppy finishing ensured the scoreline didn't change.
But the outcome was never in doubt. Arteta, along with Marouane Fellaini, bossed the midfield and will have felt the benefit of getting 90 competitive minutes under their belts after a pre-season hampered by minor niggles.
Along with Louis Saha who benefited from a 30-minute cameo, the match time for the trio will boost the manager's options when they travel to Blackburn on Saturday for their second game of the new league season.
By the time that game kicks-off the Blues will know their third round opponents, with the draw due to be made during Sky's Soccer Saturday programme.
Fellaini was the first boy in Blue to test Simonsen, forcing him into a stop low to his left with an effort from the edge of the box after four minutes.
As Everton's grip on the contest strengthened, Anichebe fired wide with a left-foot effort on the turn, Arteta did likewise, Barkley tested Simonsen from distance and Fellaini narrowly missed the target with a couple of good efforts.
The lanky Belgian was proving an imperious figure in the heart of the pitch in the early skirmishes as Danny Wilson's League One outfit struggled to cope.
Increasingly, man-handling the midfielder seemed the only way the visitors could shackle his forays forward, with the Everton coaching staff frustrated by the officials' failure to reprimand the culprits.
At the other end, United's only effort on Everton's goal in the opening 25 minutes was a speculative shot from Harry Maguire that flashed well wide of the target.
So, with the home side dominant and the visitors struggling to contain them, it was a huge shock when a counter-attack in the 28th minute resulted in the opening goal of the game.
Stephen Quinn darted down the left, produced a telling low cross and Cresswell slid in to guide a shot into the corner of Jan Mucha's goal.
Goodison was stunned. But the men on the pitch weren't. And inside three minutes they were level largely because of Jack Rodwell's efforts.
He found space on the left of the United area, curled in a low cross and a significant deflection off goalscorer Cresswell proved decisive.
And six minutes later, with 37 minutes on the clock, the scoreline was given a more fitting look when Anichebe completed a sweeping move which owed a great deal to the smart feet of Leon Osman and the blossoming Barkley.
And the youngster was involved for the third three minutes before the break. Tackled on the edge of the box as he charged forward, Arteta latched on to the loose ball to sidefoot home with aplomb.
It was no less than the home side deserved and provided a half-time scoreline more befitting their dominance.
And the flow of the game didn't change after the break. Simonsen, once the most expensive keeper in Everton history, denied his old friend Osman with a smart stop and Anichebe sent a scissor kick wide as the home side attacked their beloved Gwladys Street.
The introduction of Louis Saha for Rodwell after the midfielder picked up a knock added to the attacking impetus in Everton's play.
It was clear the contest was won. Only the margin was left to be determined.
Osman struck the upright with a snapshot from 20 yards, Fellaini had an effort deflected over the bar and sub Jose Baxter fired off-target as the home side passed their guests into submission.
But a fourth goal didn't materialise. Indeed, having surprised the Blues in the opening period, United almost scored an unlikely consolation as the contest entered injury-time.
Maguire's effort from distance had to be acrobactically tipped over the bar by Mucha, who had spent much of the evening as little more than a spectator.
Ultimately, however, a first win of the season and progression in the competition meant it was a satisfying night for the Blues.