Blackburn's victory, which included two Arsenal own goals, helped them climb off the bottom of the table while all three promoted sides won on the same day for the first time since February 2010.
Swansea City - who failed to score in their opening four matches - won for the first time, beating West Bromwich Albion 3-0 at the Liberty Stadium with Scott Sinclair scoring their first goal in the top flight since 1983 with a first-half penalty.
In the day's other matches Everton came from behind to beat Wigan Athletic 3-1 at Goodison Park while Aston Villa drew 1-1 with Newcastle United at Villa Park.
The day's opening match produced a seven-goal thriller with Blackburn twice coming from behind to beat Arsenal as Aiyegbeni Yakubu scored twice on his Rovers debut and Alex Song and Laurent Koscielny put through their own net to give Rovers the points.
Blackburn were level again after 50 minutes when Arsenal failed to clear a free-kick and the ball bounced off Song's thigh and past goalkeeper Wojciech Szczesny for the equaliser.
Nine minutes later Yakubu scored from point-blank range and was ruled onside to make it 3-2 and 10 minutes after that a stunning break from Blackburn which involved Junior Hoilett and substitute Martin Olsson ended with Olsson's cutback being turned into his own goal by Koscielny to make it 4-2.
Wenger told Sky Sports he was concerned by his team's start to the season where they have taken just four out of a possible 15 points.
"If you want to win football games you have to be focused for every minute, and that cost us today, it was very frustrating because if you look at the statistics we should have won easily," he said.
Kean told Sky: "Today we showed a lot of character which everyone has been questioning, well not everyone, just one per cent of people, about 200 who demonstrated and hopefully we can turn them around because the rest of the people who are behindus got a fantastic performance today and that's exactly what we are all about."
While emotions were running high at Blackburn, they were in Swansea too where a minute's silence was held before the start to mark the death of manager Brendan Rodgers' father and this week's tragedy at the nearby Gleision Colliery which claimed the lives of four local miners.
