David Moyes' dominant side looked set to be on their way to a disappointing draw, but after Gretar Steinsson saw red for a foul on Pienaar on 71 minutes, Arteta curled the resulting free-kick to put the Toffees ahead.
The home side had earlier found Bolton keeper Jussi Jaaskelainen in fine form but Arteta's strike - and a late second from Pienaar - ultimately sent the Trotters home empty-handed.
Bolton seized the early initiative and they had a penalty appeal on three minutes after a Steinsson free-kick bounced around the box but referee Alan Wiley was not interested.
Owen Coyle's side were on the front foot again six minutes later but Zat Knight's header was easily saved by Tim Howard.
The home side gradually started to get a foothold in the game as the half wore on - Arteta struck a free-kick into the wall while Diniyar Bilyaletdinov, a 15th minute substitute for Victor Anichebe, fired over.
But it was Bolton who wasted the best chance of the half on 39 minutes - Chung-Yong Lee and Jack Wilshere combined well to send Davies clear but the former Chesterfield frontman couldn't beat Howard.
The second half followed the scrip of the first with the home side dominating play, but struggling to find the end product, Ayegbeni Yakubu had a deflected effort saved by Jaaskelainen on 51 minutes.
And two minutes later the Bolton stopper was at it again, this time blocking a Johnny Heitinga effort.
The game exploded into life in the last quarter when Bolton were reduced to ten men when Steinsson received his marching orders for bringing down Pienaar on 71 minutes.
And the Toffees made the advantage count immediately when Arteta curled the resulting free-kick into the top corner.
Bolton tried to get themselves level, but Pienaar's 89th minute goal ensured Everton's unbeaten home run extended to nine games.