The young German, cruelly robbed of victory when he was taken down at the very last turn in Valencia, edged out Noriyuki Haga by the slimmest of margins at the end of a frantic race in which the top four were rarely covered by more than one second.
Pole sitter Troy Bayliss was passed by Neukirchner's Alstare Suzuki team-mate Yukio Kagayama into turn one - the Ducati star soon responded, but by the end of the first lap both GSX-Rs had overtaken the 1098, with Haga back in sixth after a poor start.
However, Haga soon blitzed past both Sterilgarda Ducati riders Ruben Xaus and Max Biaggi and was on the tail of the leading trio by the end of lap 2 of 18. Nori overtook Bayliss on lap 5, Neukirchner on lap 7 then countryman Kagayama - on the entry to the Parabolica - to lead for the first time on lap 8.
Haga hitting the front indicated that the double 2007 event winner might be hard to beat, but the #41 immediately found himself back under attack from the Suzukis - although Kagayama, who had straight-lined several chicanes, saw his victory charge effectively end when he out-braked himself into turn one on lap 10, dropping him back to fourth.
At the same time, Bayliss was struggling to match the pace - allowing Neukirchner and Haga to gain breathing room up front - although all four riders had closed up again as the penultimate lap began with Neukirchner leading Haga, Bayliss and Kagayama.
Haga crawled all over Neukirchner during the final circulation to try and find a way past, but the German's powerful machine gave him the edge on the straights, while Max - who had fallen victim to Haga's superior braking skills earlier in the race - raised his game to lave Nori with no possible opportunities.
A delighted Max thus took his first WSBK victory, and only third, during his fourth season in the class, with Yamaha star Haga one of the first to congratulate the German - before joking that he must have a 1200cc engine in his Suzuki!
Bayliss, making his final Monza appearance, was quick to credit both Neukirchner and Haga for their efforts - but the ever-competitive Australian was typically disappointed not to have won in front of the Italian fans and warned he'll be desperate to do so in race two.
Despite his disappointment, Bayliss has increased his title lead to 78 points over Carlos Checa - the man who brought down Neukirchner at Valencia. Checa suffered an appalling start from the front row of the grid and later straight-lined a chicane on his way to eighth position for Hannspree Ten Kate Honda.
By contrast Biaggi got a superb start from ninth on the grid, and fifth was probably better than he had expected. Team-mate Xaus had qualified sixth, but highsided at the Parabolica while battling with Biaggi early in the race.
Race results (1) - Monza: