That they have managed this despite the enforced, prolonged absence through injury and suspension of the influential Emm-anuel Petit suggests a strength of character as well as squad. He looked just a little off the pace, and his sending-off for two clumsy fouls on his compatriot Olivier Dacourt now means three more missed matches.
"It will certainly be a problem for us," said Arsenal's manager Arsene Wenger. "But we have had to learn how to manage without him."
But it was, in fact, the midfield axis of Marc Overmars and Ray Parlour that broke the deadlock and maintained the visitors' stranglehold. Just after the quarter-hour, Overmars, free on the left and a little beyond the halfway line, floated a pin-point crossfield ball to the unmarked Parlour on the right wing. His control was sure and the volleyed finish thundered past a flailing Thomas Myhre.
A minute later, Arsenal's advantage applied to players on the pitch as well as goals scored when the referee Uriah Rennie showed his first red card of the afternoon to the Everton striker Don Hutchison for the use of an elbow on Martin Keown.
Everton's manager, Walter Smith, clearly felt the decision harsh but was more concerned with its effect on his team's performance than on the loss of a key man for the long run-in. "It was going to be a tough match anyway; after losing Don so early it was a real struggle for us even to get involved," he said.
Despite being a man up, Arsenal seemed happy to bide their time. As Wenger said: "We dropped our pace, and while we were always in control we were never really dangerous."
Indeed, the wide men and Bergkamp allowed themselves the luxury of roaming the park, but to little effect. After the break, a galvanised Everton hustled hard to squeeze back into the game using a combination of the midfield muscle of David Unsworth and Dacourt and the guile of Nick Barmby and the substitute Tony Grant.
Dacourt's return to the enforcing role in a midfield shorn of much talent because of long-term injuries, was welcome to an Everton side knowing they need to battle to stay alive. His effort and persistence could not be questioned, and will be valued as the season progresses, but his rumbustious tete-a- tete with Vieira and Petit proved fruitless - a sending-off excepted.
Instead it was left to Barmby, Everton's only real threat, to proffer the kinds of sparks needed to put Everton back in the game. His incessant forays down the right and in support of the lonely Ibrahima Bakayoko went unrewarded, even after his team achieved parity with Petit's dismissal. After he departed, the game picked up as a spectacle with Arsenal seeking to press their territorial advantage. The deserved killer blow came as Parlour raced into the box with the ball under close control only to be upended by Unsworth's ungainly challenge. If there were question marks over Rennie's decision to dismiss Hutchison, there were no complaints about the penalty award and Bergkamp duly doubled the advantage, pushing the strike low to Myhre's right.
With the game now more open, flowing space was found in abundance by both teams. Arsenal could afford to enjoy this period and an audacious volley by the substitute Nelson Vivas from the corner of the box was nimbly tipped over by Myhre. Everton's late thrusts, in marked contrast, were born more of a desperate urgency. While Unsworth almost made amends for the penalty with a volley that rattled the bar, Dacourt's effort from a similar range was hit and hope.
So Everton's fight for survival continues, while their loftier opponents, without the "hindrances" of the European adventures to be enjoyed by their championship sparring partners, may begin to feel this unwanted lighter schedule will prove decisive.