Mata rifled in a low finish past City keeper Willy Caballero early in the second half at Old Trafford on a night of few chances but plenty of derby fervour as United boss Mourinho won the tactical battle against Guardiola's much-changed City side.
The result lifted some of the pressure off Mourinho following Sunday's 4-0 defeat to Chelsea, but for his old sparring partner, Guardiola, it was a sixth successive game without victory, his longest winless streak as a manager.
West Ham United also moved into the last eight after they overcame Chelsea 2-1 in a London derby spoiled by ugly scenes of fan violence at the end of the game, while Southampton heaped more misery on struggling Sunderland with a 1-0 victory.
Recent results and the gathering pressure on both Mourinho and Guardiola ensured the clash at Old Trafford had all the usual spice of a derby encounter even if City made nine changes to their side against a virtually full-strength United team.
City should have gone ahead after two minutes, but Kelechi Iheanacho darted in front of his marker to direct his header hopelessly off target from close range.
United offered little attacking threat, but gained control of possession as the match wore on and were the more dangerous side for most of the encounter.
It took until the start of the second half, however, for them to create a meaningful chance when Paul Pogba's low shot was turned onto the post by Caballero, sparking an onslaught from the home side that ended with Mata's opener on 54 minutes.
Zlatan Ibrahimovic shrugged off a challenge then played the ball back towards Ander Herrera, who went down dramatically in the box but Mata was following up to powerfully steer the ball home.
DERBY KNOCKOUT
Then it was just a case of holding on, which they did comfortably, as Mourinho recorded his fourth victory over Guardiola in a rivalry spanning 18 matches.
The greater satisfaction for the Portuguese, however, seemed to be erasing some of the negativity of Sunday's thrashing by his former club Chelsea.
"The fans felt deeply such a negative result and today was a good chance to clear that feeling because a derby knockout and to win gives everyone a better feeling," he said.
West Ham's woeful start to the season is turning round and the revival continued in the first derby at their new London Stadium home.
Tight security arrangements, including a ban on the sale of alcohol in the vicinity of the Olympic Park, was intended to prevent flashpoints off the pitch, but there were still ugly scenes towards the end as rival fans clashed behind the goal with several seats being ripped out.
On the pitch, a vibrant West Ham proved too strong for a Chelsea side much-changed from their weekend trouncing of Manchester United.
Cheikhou Kouyate put the Hammers on their way to a third consecutive win with a thumping header from skipper Mark Noble's driven cross after 11 minutes and Edimilson Fernandes beat Asmir Begovic with a low shot three minutes after the restart.
Gary Cahill did grab a Chelsea consolation in stoppage time but by that time all eyes were on stewards trying to keep rival fans apart.
Southampton's record signing Sofiane Boufal scored from long range in the second half in their 1-0 victory over Sunderland, a fourth defeat in five games for Sunderland manager David Moyes.
(Reporting by Toby Davis, editing by Pritha Sarkar)
source: www.abs-cbnnews.com
