Arteta opened the scoring in the Premier League clash after Santi Cazorla went down after a challenge by Steven Reid, although replays showed the defender did not touch his opponent.
Arsene Wenger's team doubled their lead in the second half when Alex Oxlade-Chamberlain was fouled by Chris Brunt and Arteta scored from the spot again.
Victory moved Arsenal up to sixth place, two points below the top four, after a sequence of one league victory in six matches had seen them slide down the table to 10th.
The Frenchman was able to bring back his key players after resting the likes of Jack Wilshere and Arteta for the Champions League defeat at Olympiakos in mid-week.
He was also able to recall Bacary Sagna from a foot problem and Lukas Podolski was on the bench after recovering from a hamstring complaint.
West Brom were forced into a change after just seven minutes of action when Liam Ridgwell picked up an injury, with Goran Popov coming into a defence put under early pressure.
Cazorla was at the heart of Arsenal's attacks, firing wide with his first attempt after Wilshere slid the ball to him on the edge of the area.
The Spaniard also volleyed over after Oxlade-Chamberlain burst down the right and drove in a cross that was met first-time by his team-mate.
Cazorla was inevitably involved in the opening goal in the 26th minute, although West Brom were furious when referee Mike Jones awarded the penalty.
Reid flicked out a leg as Cazorla checked back in the area onto his right foot, but replays showed the Arsenal midfielder was not touched as he threw himself to the floor.
Arteta was not affected by the protests and coolly chipped his spot-kick down the middle.
It was his second goal of the season and came a month after he had an injury-time penalty saved against Fulham.
West Brom felt they should have had a penalty when Per Mertesacker handled the ball, but Jones had already whistled for a foul on the Germany international.
Boaz Myhill also saved from Gervinho, while Oxlade-Chamberlain volleyed over acrobatically just before the break.
West Brom put Arsenal under pressure in the second half and Gareth McAuley went wide with a header.
But the hosts were two goals ahead in the 64th minute when Oxlade-Chamberlain raided down the right and went down under Brunt's challenge.
West Brom felt the England winger had committed a foul in the build-up but there was no dispute over the penalty decision, and Arteta chipped down the middle again to seal the points.
Markus Rosenberg came off the bench for the visitors and felt he was tripped in the penalty area, but Jones waved play on this time.
Romelu Lukaku was also introduced as a substitute as West Brom chased the game but Arsenal held on and could have easily added another goal.
Lukaku went wide with a header with the visitors' best late effort, while Podolski came on and blasted over from close range.
Source: AFP
Source: AFP