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The game had appeared to be heading towards stalemate until the 70th minute when Bolton full-back Gretar Steinsson hauled down Aiyegbeni Yakubu as he chased towards goal in pursuit of a Steven Pienaar through ball.
Referee Alan Wiley showed Steinsson a straight red card and Arteta added to the punishment by placing a superb 20-yard shot past the Bolton wall, leaving goalkeeper Jussi Jaaskelainen rooted to the spot.
The last-minute second goal, from Pienaar, arrived as the South African slotted the ball into an empty net from 15 yards after substitute Leon Osman did well to keep the ball alive on the by-line.
Bolton, buoyed by a recent run of three victories from their last four games which has lifted them up the table, made a confident start and might have had a penalty as early as the third minute after Steinsson's free-kick into the home area caused a scramble.
Johan Elmander's shot was blocked by Phil Neville and, as Kevin Davies attempted to turn the loose ball towards goal, it appeared to hit the arm of John Heitinga although no spot kick was forthcoming from Wiley.
Victor Anichebe soon had a chance to ease the pressure on Everton as he chased down Tim Cahill's through ball but, with only Jaaskelainen to beat, the Everton forward’s first touch took the ball out of his control and allowed Bolton full-back Paul Robinson to make a crucial tackle.
It was not Anichebe's day because he was soon badly fouled by Robinson, out on the right-hand touchline, and was stretchered off soon after, still suffering from the effects, to be replaced by Dimitar Bilyaletdinov.
Robinson should have been booked for that challenge but, much to the anger of the home supporters, Wiley made Cahill his first yellow card for a crude lunge at Jack Wilshere as the game took on a fairly physical edge.
That particular infringement might have proved costly as Davies headed goalwards and Phil Jagielka had to make a spectacular clearance, producing a clearing header over his own bar.
Bolton looked dangerous from such set-pieces and Zat Knight had almost poked in a Lee Chung-Yong free-kick at the far post.
Everton, for their part, were short on chances and the home crowd becoming restless - a wild shot over from Pienaar summing up their frustration.
At the other end, Baines headed a Davies centre away from goal, but only as far as Tamir Cohen whose first-time snap shot fizzed over the bar.
Then a flowing Wanderers move ended with a back heel from Chung-Yong, a neat pass from Wilshere and Davies surging through only to see his shot kept out by Tim Howard's outstretched leg.
Everton opened the second half with more urgency with Yakubu forcing a save out of Jaaskelainen.
Then Jagielka wasted a glorious chance to open the scoring when he met Arteta's free-kick, unmarked six yards out, but guided his header straight at the keeper.
Arteta struck soon after and the ten men of Bolton would have been in even deeper trouble had Osman not struck the bar with the goal at his mercy a minute before his team’s second goal.
