Nasri scored the opener and was their creative heart as this time Leeds failed to cope with qualities of their Premier League opposition.
Bacary Sagna's cracking drive made it 2-0 and Leeds were left only with the memories of Bradley Johnson's blistering strike to sweeten the bitter pill of defeat, especially when Robin van Persie came off the bench to round off the scoring.
After struggling against Leeds at home in this FA Cup third-round contest, and having been embarrassed at Ipswich in the Carling Cup last week, this was a far more comfortable ride. That was thanks in large part to France international Nasri, whose presence in midfield looked hugely reassuring.
It took less than five minutes for the 23-year-old to make a telling impact and score his 14th goal of the season.
Andrei Arshavin, who had a point to prove after some dismal recent performances, played a key role in the move, with Marouane Chamakh stepping over his pass to allow Nasri to dance through and slip the ball neatly to the side of Kasper Schmeichel.
We did not let up however and Leeds were chasing elusive shadows for much of the game.
Simon Grayson's men were kept in it by Schmeichel's stunning save, scooping Chamakh's downward header off the line. The Moroccan continued, however, to be a thorn in Leeds' side with a blistering run down the right and penetrating ball that somehow Arshavin failed to turn home.
The Russian tried to make amends but once more Schmeichel came to the rescue, turning aside his fierce low strike.
Anything Arshavin could do, Nicklas Bendtner was keen to show he could do better, but the Dane's miss from Sagna's pinpoint cross was if anything even more ghastly than Arshavin's minutes earlier.
"That's why you're 52," chanted the Leeds fans in reference to Bendtner's shirt number.
When Sagna drilled home into the top corner with the outside of his right foot to make it 2-0 it seemed as though Arsenal were home and dry.
But Leeds, who had barely ventured into our half, were suddenly back in the running thanks to a quite stunning long-range strike by Johnson, who began his football life an Arsenal schoolboy but was released as a 15-year-old.
Johnson, who made his way to Leeds via non-league football, Cambridge and Northampton, will not have hit a more glorious shot in his life. Struck with the left foot from 30 yards out, it screamed into the top right corner with goalkeeper Wojciech Szczesny clawing at thin air.
That gave Leeds some hope at the break but Nasri picked up the threads again immediately. His lovely disguised pass put in Alex Song inside the opening 30 seconds, but Schmeichel beat away the strike.
Schmeichel then had to be alert to keep out Nasri's free-kick but the Arsenal hordes kept coming. One beautifully-crafted move saw Nasri so nearly send Arshavin clear only for a last-ditch interception by Robert Snodgrass.
Arshavin's desperation for a goal can only have increased when he tried a first-time shot from Song's pass only to see it soar not only over the bar but actually out of the ground, to raucous jeers from the Leeds fans.
Max Gradel and Billy Paynter had had no change out of the our defence but they almost combined to good effect with 20 minutes left to serve a warning that this game was not over.
Perhaps stung by that, Wenger left nothing to chance as he sent Cesc Fabregas and Van Persie on for the last 15 minutes, and Spaniard Fabregas almost immediately forced Schmeichel into a save from a direct free-kick.
Van Persie's first touch was even more decisive, the Dutchman heading powerfully home from Bendtner's cross to finally end the contest.
We had triumphed 4-1 in their last three appearances at Elland Road and Kieran Gibbs looked set to bring about a repeat scoreline with his first goal for the team but his low effort trickled wide.