The Gunners manager had never got the better of his Portuguese counterpart in eight previous meetings, and that figure became nine courtesy of goals either side of half-time from Cesar Azpilicueta and Juan Mata.
The result saw the home side fail to reach the quarter-finals of the competition for the first time since 2002, but they paid the price for failing to convert pressure, especially in the second half, into chances.
Wenger made eight changes to the side that started last Saturday's win over Crystal Palace, with the trio of Laurent Koscielny, Aaron Ramsey and Santi Cazorla keeping their places.
Meanwhile, Mourinho's unhappiness at having to send a team out barely 48 hours after the last-gasp win over Manchester City was reflected in a team selection that featured just Gary Cahill from the 11 that walked out at Stamford Bridge over a day after Arsenal had left the Selhurst Park pitch.
The host of changes by both managers meant two of the country's top sides using many players with little game-time under their belts as October edged towards November, but it was Chelsea who looked the far more comfortable as the game unfolded.
The west London outfit won a string of early corners as they enjoyed the best of the possession without troubling Lukasz Fabianski in the home goal. At the other end, the hosts failed to test Chelsea's oldest-ever player, 41-year-old Mark Schwarzer making a rare appearance as Petr Cech was rested.
But Chelsea took the lead on 25 minutes through an unlikely source as yet again a defence facing the Blues conspired to present them with a gilt-edged chance to score.
The confusion as Carl Jenkinson failed to decisively deal with a ball dropping on the edge of his box had shades of the Joe Hart-Matija Nastasic incident two days earlier, but this time it was Azpilicueta, racing upfield from defence following a corner, who was on hand to touch the ball in off the post for his first Chelsea goal since his move from Marseille in August 2012.
The goalscorer soon allowed fellow Spaniard Nacho Monreal a shooting chance, but his raking effort following a mistake from the Chelsea defender flew across Schwarzer's goal and just wide after a slight touch off Gary Cahill.
But the goal failed to spur Arsenal on into a concerted response, with Nicklas Bendtner cutting an isolated figure up front, while Chelsea were quick to snuff out any home attacks. In fact Mata, required to put in a shift when his side are without the ball by his manager, personified Chelsea's committed approach.
A deflected shot from Ramsey that bobbled wide early in the second half lifted the home fans and led to their side's best spell so far. But failure to pressurize Schwarzer, particularly by Bendtner, led to more frustration and continually let Mourinho's men off the hook.
Ramsey pulled a shot wide seconds before Mesut Ozil replaced the anonymous Ryo Miyaichi on the hour as Wenger looked for his side to properly assert themselves. However Mata's brilliant strike shredded the script marked "comeback", the Spain international taking one touch to control the ball after it skimmed off Willian's head before rifling an unstoppable drive past Fabianski from the edge of Arsenal's area.
Olivier Giroud drove a shot at Schwarzer, but another substitute in Ramires came close to extending Chelsea's lead within seconds, his fine dribble only thwarted when Koscielny luckily squeezed the ball to safety after treading on it.
The away side held their hosts at arm's length for the rest of the match, and ended the evening as comfortable winners to the delight of the 9,000 fans that had made the short journey across the capital.