Arsene Wenger's side is in fine form and Van Persie leads the way with his 29th goal in this calendar year and two assists as the Baggies are easily dispatched.
Thomas Vermaelen and Mikel Arteta were the beneficiaries from their captain's creative display, though a fine performance from Carl Jenkinson at right back did not go unnoticed.
The home side started brightly, dominating possession as is customary at the Emirates.
A real buzz came over the crowd whenever Van Persie came into contact with the ball, but the home side failed to trouble Ben Foster in the opening stages, Andre Santos hitting over from a free kick with the only effort of the first 10 minutes.West Brom was momentarily down to 10 men as Jonas Olsson went off to receive treatment for a facial injury after colliding with Thomas Vermaelen, but the defense held strong with Steven Reid dropping into center back until Olsson was ready to resume.
But in the 23rd minute, Arsenal was rewarded for the calm buildup play, as Mikel Arteta beautifully sliced open the West Brom defense to find Theo Walcott.
The winger tried to slot through Ben Foster's legs, but his attempt was stopped, only for Van Persie to tap in for his 11th goal of the Premier League season.
That goal served to buoy both the Arsenal team and the fans, with Jenkinson putting in some dangerous crosses down the right wing, and generally impressing.
And five minutes before halftime, the Gunners doubled their lead. West Brom failed to clear its lines after a corner, and Alex Song drifted a cross over to the back post where Van Persie was waiting to cut the ball back across goal for Thomas Vermaelen to apply the finish.
After Chris Brunt missed the Baggies' best chance of the game, volleying well over from the edge of the box, Arsenal almost made it three as Gervinho found Aaron Ramsey in the box before the Welshman turned and dragged a shot just wide of the post.
The game was well and truly put to bed after a double change from Arsenal, and Tomas Rosicky played a key part, finding Van Persie in the box, where his layoff was perfect for Arteta to sweep a shot into the corner.
West Brom did cause some trouble as Somen Tchoyi came on and had a shot blocked with a sliding tackle from Vermaelen, but the striker really should have done better, as Vermaelen was already on the floor when his shot was struck.
The rest of the match fizzled out with Szczesny occasionally called upon to make a stop, but rarely troubled as the Gunners sealed another win.