Mourinho inflicts more woe on old rival Wenger.
There was nothing lucky about the second, however, as Juan Mata showed some fine skill before lashing home a right-footed shot.
It was a second successive home defeat for Premier League leaders Arsenal who face inform Liverpool on Saturday. Revived Chelsea go to ailing Newcastle at the weekend.
Fulham's patchy form continued as they were knocked out by Leicester in a 4-3 thriller at the King Power Stadium in their fourth round clash.
Hugo Rodallega gave Fulham an early lead but Leicester scored three in quick succession either side of half-time to take control.
Wes Morgan levelled in the 41st minute after Maarten Stekelenburg failed to hold a free-kick and Chris Wood put the Foxes ahead just before halftime when a blocked clearance fell kindly.
Then Miguel Ignasi headed in a third in the second half before Rodallega's quickly responded for Fulham then Giorgos Karagounis levelled with a late freekick.
But no sooner were they level than Lloyd Dyer struck what would prove the winner.
West Ham edged out Championship leaders Burnley 2-0 at Turf Moor with both goals coming from the penalty spot late on.
Matthew Taylor got the first in the 76th minute after Jason Shackell brought down Kevin Nolan while Jack Collison tucked away the second in stoppage time after being fouled by Keith Treacy, who saw red to complete Burnley's misery.
Manchester United eased through after dispatching Norwich 4-0 at Old Trafford. Javier Hernandez scored twice to strengthen his claims for more pitch-time. The Mexican got his first from the spot after Leroy Fer needlessly felled Adnan Januzaj, then headed in a second on the rebound early in the second half.
Phil Jones volleyed in a third but by then, Norwich were more concerned by the condition of Robert Snodgrass, taken off on a stretcher wearing a neckbrace, after a lengthy stoppage which followed a clash of heads.
The incident led to 11 minutes of added time being played, and United used them to add a fourth through substitute Fabio.
Stoke needed penalties to see off the 10 men of Birmingham at St Andrew's after Blues scored twice in the last five minutes to force extra-time, then equalised again in the 118th minute to make it 4-4. Oussama Assaidi got the match off to a fine start with a 30-yard screamer and although Tom Adeyemi levelled for Birmingham, they seemed doomed as Stoke took control after Wade Elliott was sent off on the stroke of half-time.
Mark Hughes' side used the extra man to set up Crouch's 55th-minute header and Arnautovic's 71st-minute strike.
Crouch then hit the bar before Peter Lovenkrands tied it with goals in the 85th and 90th minutes.
And although Kenwyne Jones put Stoke back in front four minutes into extra-time, Olly Lee rifled home another late equaliser.
But Birmingham's brave effort fell short as Mitch Hancox and Callum Reilly missed their first two penalties, and clinical Stoke won the shoot-out 4-2.
Arsenal's Jack Wilshere (left) and Chelsea's John Obi Mikel battle for the ball as Juan Mata looks on during last night's Capital One Cup, fourth round match at the Emirates Stadium