He was right, except that the fortune came in spades on a bright autumn afternoon in west London.
The most bizarre of own goals from Steve Marlet and a series of generous decisions by referee Jeff Winter which deprived Fulham of what appeared at least one certain penalty helped Arsenal to avoid their worst sequence of results for 25 years and stay in touch with Liverpool at the head of the Premiership. It was hardly surprising that it wasn't vintage Arsenal.
Their confidence had been significantly dented by four consecutive defeats in what was a distinctly Black October for the red half of London which made a mockery of Wenger's boast that his side could go through the entire season undefeated.
Another loss here would have equalled the club's worst run for 25 years. And for large parts of what was a tense and thrilling London derby Arsenal's victory looked anything but assured.
Fulham these days, especially in the intimate surroundings of Loftus Road, are anything but a soft touch and their own confidence could not have been more buoyant following their 3-0 midweek away triumph in the UEFA Cup against Zagreb.
But try as they might they could not quite find the cutting edge to capitalise on Arsenal's fragility which emanates mainly from uncharacteristic problems in defence where Sol Campbell and Pascal Cygan have not formed the rock-like foundation of past Arsenal partnerships.
Arsenal, however, even amid their run of defeats, had been making chances and playing the flowing football which has become their hallmark under Wenger.
They simply hadn't been hitting the back of the net with the same regularity of last season and even with Dennis Bergkamp starting his first match since his recent Achilles tendon problems the same flaws appeared to remain.
As it was Fulham should have taken the lead in the first minute, Steed Malbranque floating over a pinpoint cross which eluded the Arsenal defence and fell invitingly onto the head of full-back Steve Finnan at the edge of thesix-yard box.
It seemed the easiest of tasks for Finnan to direct his header past goalkeeper David Seaman but instead he proceeded to send it a couple of feet over the crossbar.
Fulham perhaps should have realised it was not going to be their day from that moment.
If not, then they certainly had reason to feel aggrieved in the ninth minute when they should have been awarded a penalty.
Tidy work by former Arsenal striker Luis Boa Morte took him deep into the Arsenal area and, with a little chip over one defender and a headed nudge past another he seemed to have worked a shooting opportunity. Just as he set himself, however, England central defender Campbell arrived like an England rugby flanker to barge him out of the way with a tackle which would have graced Twickenham.
Inexplicably, referee Winter waved play on. If that was fortunate then when Arsenal took the lead in the 31st minute it was in the most bizarre fashion.
Thierry Henry failed to get any height on a corner from the left and it should have been cleared with ease by the Fulham defence.
It was perhaps Henry's worst delivery from a set-piece this season, except that as it swept at ankle height into the Fulham six-yard box Marlet took a mighty swing at the ball and only succeeded in deflecting it cruelly past the stranded van der Sar.
Golfers who have ever experienced an embarrassing shank on the first tee at the weekly medal will know exactly how Marlet must have been feeling.
From such outrageous strokes of fortune are football matches won and lost and perhaps this was the one Arsenal needed to end their disastrous run.
To be fair they had other chances, van der Sar being called upon to save with his legs from first Henry and then Ljungberg and Seaman barely had a save to make throughout the 90 minutes despite mounting Fulham pressure.
Fulham, however, had legitimate appeals for another penalty in the 50th minute when Campbell again seemed to catch the foot of the elusive Boa Morte on the edge of the area.
Referee Winter again waved away appeals.
Despite a relentless Fulham onslaught which saw Japan's Junichi Inamoto thrusting forward and Sylvain Legwinski go close with a header there was a certain inevitability to Arsenal's victory.
It left Wenger wearing a smile for the first time in almost a month though referee Winter was surrounded by protesting Fulham players at the end of the match and received a vitriolic reception from fans as he walked down the tunnel.
Fulham rightly felt hard done by.
But while it was not exactly normal service yet for the Gunners, too uncertain and lacking in rhythm, they are at least back to winning ways.
For that Wenger was truly thankful.