Following a sluggish start to the new campaign, Wenger's men have now picked up seven points out of nine and looked more like the outfit which produced a strong finish to last season, reaching the Champions League final after clawing themselves back to fourth place.
However, despite a comfortable scoreline in the end, the Gunners were made to work hard for an hour by the battling Blades, who stay rooted to the foot of the table.
Eventually, though, Arsenal's patience paid off with William Gallas firing in his first goal for the club, an own goal from United captain Phil Jagielka and Thierry Henry's late header then sealing victory for Wenger, who celebrates 10 years at the club next week.
After seeing Chris Armstrong's early 25-yard free-kick comfortably saved by Jens Lehmann, the home soon settled.
The ball was worked down the left flank to Tomas Rosicky, who fed the ball inside to the on-rushing Gallas just outside the box.
In the 14th minute, Blades keeper Ian Bennett produced a brilliant stop to deny Henry, fit again following two games out with a foot injury.
Kolo Toure scampered away on the right, and sent over a lofted pass to the far post. The Arsenal captain arrived on cue with a deft header back across goal - only for Bennett to somehow get enough of his hand on the ball to deflect it to safety.
The visitors were being forced to defend deeper all the time.
However, despite all their possession, Arsenal were unable to find a telling pass in the final third - much to the frustration of the Emirates faithful.
After 30 minutes, Cesc Fabregas was cautioned by referee Alan Wiley for a late challenge on Jagielka.
Fabregas was then in the wars himself, needing treatment for a blooded lip after he was stepped on by Armstrong after falling over during a tussle in the centre circle - ruled accidental by Wiley.
United thought they had scored towards the end of the first half when Mikele Leigertwood lashed in a stunning half-volley from the edge of the area after the ball dropped following a corner. However, the whistle had already been blown because of dangerous play against Hulse, for an attempted scissors-kick in the six-yard box.
Arsenal started the second half brightly, Toure flashing a shot just wide.
Then, on 52 minutes, Bennett produced another fine reaction save to tip over Freddie Ljungberg's header.
There was a warning for Arsenal as the hour mark approached following a rare attack by the visitors.
Hulse had time and space on the edge of the area to chip an effort goalwards, which drifted wide with Lehmann off his line.
The home faithful continued to grow more frustrated as despite plenty of effort, Wenger's side could not break down the United rearguard.
Finally, though, Arsenal got the breakthrough with 25 minutes left following a well-crafted move.
Henry chipped the ball into the area for Fabregas, who in turn took one touch to tee up Gallas - and the defender volleyed past Bennett for his first goal since joining from Chelsea on deadline day.
Having worked so hard to get in front, Arsenal looked determined to close out a first Premiership win at the Emirates.
And the points were wrapped up on 69 minutes.
Henry again weaved his way into the left side of the area and to the touchline, before cutting a pass back across goal.
Jagielka took an almighty swing - but could only manage to spin the ball with the outside of his foot into the far corner.
Henry made it 3-0 when he headed in Emmanuel Eboue's cross with nine minutes to go.
Lehmann produced a fine save at the far post in stoppage time to deny substitute Steve Kabba a consolation goal in front of the massed ranks of travelling United supporters.