A 78th-minute Aaron Ramsey own goal and a late Luis Suarez strike gave Liverpool a win that piled on misery in a bad week for Arsenal, who ended with 10 men for a second league game in a row after Emmanuel Frimpong was sent off 20 minutes from time.
They had already suffered misfortune a quarter of an hour into the match, when they lost defender Laurent Koscielny to a back problem, bad news for a side already ravaged with injuries, suspensions and reeling from the departure of Cesc Fabregas.
"It's very difficult to take on the chin that defeat, because with the effort we put in I don't think we deserved to lose the game," Wenger told the BBC after his team left the pitch to boos after Liverpool's first ever win at Emirates Stadium.
"We cannot say at the moment we are very lucky."
Fortune was, however, with Chelsea in manager Andre Villas-Boas's first league match at Stamford Bridge.
The hosts trailed from the fourth minute, when Alex lost the ball to West Brom striker Shane Long, who scampered through and wrongfooted stand-in keeper Hilario to claim his second goal in two games since joining the club this month.
Chelsea pulled level when Nicolas Anelka's low shot took a deflection off defender Jonas Olsson in the 53rd minute and Malouda completed the rescue mission when he arrived at the back post to sidefoot home a Jose Bosingwa cross on 83 minutes.
They had been lucky that an organised West Brom team had squandered a golden chance to go two goals up midway through the first half.
Long, whose early goal followed last week's effort against Manchester United, overhit his cross after an inch-perfect pass from Chris Brunt to let Chelsea off the hook.
MENTAL BLOCK
Villas-Boas had recognised early on that his sluggish side lacked spark, bringing on Malouda after just half an hour in place of the ineffective Salomon Kalou.
"We just felt it was necessary maybe to surprise our opponent in that way," the Portuguese told ESPN of his decision to make the early change.
"Most of all our first half was a mental block rather than anything else, and the players were able to free themselves from that to perform to the best qualities and the best talent."
Chelsea were a different side after the break, with West Brom keeper Ben Foster parrying an Anelka shot before defender Steven Reid blocked Malouda's follow-up.
"Our focus now is to get this performance in 90 minutes," Villas Boas added after a second successive game where Chelsea only came to life in the second half following last week's 0-0 at Stoke City.
Elsewhere, the first Premier League match in Wales ended 0-0, as lively Swansea City held firm in the face of a late Wigan Athletic onslaught, while Aston Villa marked manager Alex McLeish's first home game with a 3-1 win over Blackburn Rovers.
Newcastle United won the North-Eas
