Captain Robin van Persie fired a hat-trick and England youngster Alex Oxlade-Chamberlain grabbed a brace in the win.
The Gunners - who had not won in the league this year - raced ahead after just 79 seconds through Van Persie, but a fine free-kick from Morten Gamst Pedersen brought struggling Blackburn level.
Arsenal were soon back in front when Van Persie netted again from close range, before Oxlade-Chamberlain extended the lead five minutes before the break.
Gael Givet then saw red for a two-footed challenge on Van Persie, and there was no way back for Rovers.
Arsenal dominated the second half, as Mikel Arteta and the impressive Oxlade-Chamberlain were both on target with Van Persie collecting the matchball following a neat near-post finish just after the hour.
Substitute Thierry Henry capped a memorable afternoon when he swept home goal number seven in stoppage time to send Arsenal up into fifth place, two points behind Chelsea who host Manchester United tomorrow.
Wenger, though, wants to keep things in perspective.
"I do not give much importance to the seven goals, it is just we won and played well," said the Arsenal manager.
"I felt that recently we had quite good performances but did not get the results.
"Today we got the performance and the result, which is ideally what you want."
Wenger added: "We remained serious and were guided by the way we want to play football and not by any extravagant individualism.
"We were mature and serious, we played together until the end."
Oxlade-Chamberlain, 18, produced another all-action display, which will again fire up calls for his fast track into the senior England squad.
Wenger said: "Chamberlain has made a big step in the last months. He produces team play, he is not only going forwards, he is contributing to the defending and has improved very quickly.
"He is a fighter as well, with personality, and is much more mature now."
Henry is on loan from New York Red Bulls, and looks set to have played his final game back at Emirates Stadium.
However, Wenger indicated that could yet be extended to take in the visit of Tottenham on February 26.
"I haven't looked at it, maybe the maximum possibility we have is two more weeks. Normally no [he would not be here for the Tottenham game]," the Arsenal manager said.
For beleaguered Rovers boss Steve Kean, there were few positives.
"Trying to compete here with 11 is hard enough," said Kean, who decided to leave wantaway defender and captain Christopher Samba out of the squad.
"The sending off was not a tough decision for the referee to make because we all know the rules now.
"After that, it was a long afternoon."
Kean added: "Gael is cut up, he is a genuine guy and a very committed player, so he is very down at the moment.
"We picked up a injury to Jason Lowe, Givet will now be suspended for three matches so it was costly for us.
"This was the first time we really got turned over, so we will have to analyse it and respond.
"I could shout at the players in the dressing room, throw tea-cups at them, but the hard work starts again preparing for the next game.
"The players know they have let themselves down and we will be looking to get back to work as soon as possible."