The Russian netted the Gunners' second after an own-goal by Andre Ooijer gifted Arsenal the lead in just the second minute.
Substitute Emmanuel Eboue swooped twice in the final two minutes, once from the penalty spot, to seal all three points and extend Arsenal's unbeaten run to 15 games.
The result saw Arsene Wenger's side into fourth place while Rovers remain perilously close to the drop zone on 30 points, just one ahead of Stoke who occupy the final relegation spot.
The hosts got off to the best possible start, Arshavin apparently bundling the ball over the line after the effervescent Theo Walcott had delivered a cross into the danger area.
Initially the goal was given to the Russian but was later credited to Blackburn defender Ooijer, the Dutchman having got the final touch in the near post scramble.
Walcott posed a constant danger throughout and the England international appeared to enjoy getting the upper hand on three different left-backs employed by Blackburn over the 90 minutes - Gael Givet, Stephen Warnock and then Martin Olsson.
Givet and Warnock were both forced off through injury, although their departures from the pitch may well have come as a relief to both of them, given the run-around Walcott had given them.
But for all his pace and skill, for the most part the flying winger still lacks an end product - the shot he dragged wide of the mark just after the break was testament to that.
That chance came at the start of a dominant period of play for Arsenal, during which Walcott teed up Nicklas Bendtner to slice wide of the mark before himself launching a flying volley which Paul Robinson had to paw round the post.
While Walcott was busy wooing the crowd, Bendtner could do nothing right and he infuriated the assembled masses with a string of misses that smacked of a player lacking confidence.
The Dane's best chance of the day came in the 64th minute when he was played through on goal but he was foiled by Robinson, who was quick to come off his line.
A minute later, Arshavin showed him how to do it with a brilliant piece of finishing having beaten his man Danny Simpson at the by-line. The playmaker advanced on goal, waiting for Paul Robinson to go to ground before lifting the ball into the roof of the net.
Bendtner was withdrawn 15 minutes later and with he could only watch from the bench as Eboue - on as an 83rd minute replacement for Samir Nasri - found the net twice in four minutes.
The two chances were the type an out-of-sorts striker dreams about, the first being laid on a plate after Robinson could only parry Arshavin's shot into Eboue's path. All that was left to do was stab over the line.
And then the Ivorian stepped up to convert a penalty in the second minute of time added on after Carlos Vela had been tripped by a clumsy Olsson challenge.