Arteta, who had a recent spell as captain, has only scored one goal himself this season.
Everton went ahead seven minutes later when Lescott turned home Arteta's cross at the near post.
Mikel Arteta's early free-kick and two second-half strikes from Tim Cahill put the Toffees in command.
"He had a tough time with a really bad injury and people forget that, " Arteta told BBC Radio Merseyside.
With Mikel Arteta withdrawing from the Rangers squad through injury, Bob Malcolm was given a midfield role.
England coach Fabio Capello was thought to be keen on picking Spaniards Manuel Almunia and Mikel Arteta.
Cahill was always a threat at set-pieces and he rose to head Arteta's free-kick just off target.
Arteta has been a key figure for Everton this season, making 31 appearances and scoring seven goals.
Arteta believes the Blues' performances merit much more than the three points they have collected from their first six games.
It was left to Yakubu to level from Mikel Arteta's free-kick, extending both sides' unbeaten run to five games.
Yakubu headed in Arteta's cross after 64 minutes before Roque Santa Cruz slid in from close range two minutes later.
Tim Cahill scored a trademark header after a neat build-up between Mikel Arteta and Leighton Baines, who provided the cross.
Rathbone said Arteta will get first-class treatment as the club look to get their prized asset back to full fitness.
The Toffees only just shaded the first half and Mikel Arteta's deftly struck shot was well saved by Mark Schwarzer.
David Dunn's spectacular strike put Blackburn ahead after 22 minutes, but Mikel Arteta's free-kick beat Paul Robinson on the stroke of half-time.
And Everton killed City off on 85 minutes with an electric counter-attack in which Cahill and Arteta once again combined to devastating affect.
In contrast to Everton's tight defensive line, Arteta and Cahill were able to pick holes and expose frailties in the home side's rearguard.
Everton's Steven Pienaar hit the bar soon after while from Mikel Arteta's smart free-kick Jack Rodwell glanced a second-half header just inches wide.
Joos Valgaeren cleared Fernando Ricksen's deflected shot to Arteta and the Spaniard's low drive from 22 yards slipped under the body of Douglas.
Everton forced James into his first serious save after 66 minutes, Mikel Arteta curling in a 25-yard free-kick which the England goalkeeper held comfortably.
The equaliser came instantly, although Cahill was not involved, Distin's header from Arteta's free-kick sneaking past Hart, who should have done so much better.
Everton were posing all the threat, with Arteta forcing a diving save from Friedel and Osman driving only inches wide from the resulting corner.
Everton boss David Moyes welcomed back Tim Cahill after a two-month injury lay-off but the Toffees sorely missed the suspended Mikel Arteta's creativity in midfield.
Gavin Rae tripped Arteta 30 yards in front of goal and Ricksen forced a good save out of Julian Speroni at the expense of a corner.
Arteta swerved in a stunning free-kick from a tight angle, but questions must be asked of the positioning of England keeper Robinson on his Blackburn debut.
Yakubu set Arteta free on the left flank, then raced to the far post to get on the end of a perfect cross and head beyond Robinson.
City raised the tempo in the second half but after finding no way through, Arteta slotted home a fine second after a superb run from Jack Rodwell.
Both sides had opportunities to score seconds after the break, with Howard saving well from Bentley and Friedel blocking Fernandes' shot with his legs from Arteta's cross.
Arteta was sent off for twice stamping on defender Jara after he was brought down rather recklessly by the Chilean, but Moyes refused to discuss the incident.
BBC: Referee got key decision wrong, says Everton boss Moyes
Everton, with Mikel Arteta their conductor in central midfield, were showing the neater passing play against a Birmingham side looking solid without carrying much of an attacking threat.
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