Former Liverpool and Chelsea striker Fernando Torres scored the pivotal goal on 72 minutes as Atletico moved within eight points of leaders Barcelona.
Antoine Griezmann put Atletico ahead and Denis Cheryshev equalised for Valencia before Torres struck.
Valencia had Anderlan Santos sent off on 80 minutes before Yannick Carrasco completed the scoring.
Neville suffered just a second defeat in seven games as goalkeeper Diego Alves endured a tough night.
Atletico made the brighter start so it was no real surprise when they went ahead in the 24th minute.
They squandered possession 25 yards from goal and Griezmann let fly with a low shot that crept inside the near post with home goalkeeper Alves slow to react.
The lead lasted just four minutes, however, before Valencia scored as a long pass was cushioned by the head of Paco Alcacer to Cheryshev, who lashed home a left-footed drive from 15 yards.
Cheryshev lifted a shot over the crossbar from another Alcacer header seven minutes before half-time as Valencia grew in confidence.
Alcacer had a chance to put Valencia ahead just before the hour mark when he latched onto a pass by Sofiane Feghouli but fired straight at goalkeeper Jan Oblak.
Moments later Alves made up for his earlier error with a fantastic, one-handed save to keep out a powerful effort by Luciano Vietto.
But the keeper could do nothing to stop substitute Torres, who was making his 300th Atletico appearance, putting his side ahead with 18 minutes remaining as he slid in at the far post to turn the ball home after Jose Maria Gimenez flicked on a corner.
Santos saw red for two bookable offences with five minutes remaining and Carrasco made it 3-1 five minutes later when he fired straight at Alves, who allowed the ball to creep in under his legs.
Earlier in the day, Barcelona kept up their run with a comfortable win at Eibar.

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The 24-year-old missed the Indian Premier League (IPL) auction last month in order to concentrate on his international future.
Vince has played three T20 matches so far for England, scoring 125 runs, with a strike-rate of 119.04.
"If it's a platform to go on and play other formats for England, then that'll be ideal," he told BBC South Today.
"First and foremost, I'm going to try and help England win the World Cup and try to learn off some very good players when I am out there.
"It will be a good experience and one I cannot wait to start."
County team-mates Liam Dawson and Reece Topley have also travelled to Mumbai with the England T20 squad.
All-rounder Dawson, 26, was included despite head coach Trevor Bayliss admitting he had never seen the all-rounder play competitively, while left-arm paceman Topley was preferred to Chris Woakes.
Led by captain Eoin Morgan, England's first match will be against the West Indies on 16 March, with Sri Lanka and South Africa and a group winner from the first-round qualifiers their other Super-10 opponents.
"I think having it in the unofficial home of cricket is massively exciting," said Topley, 22. "It's going to be brilliant and it's definitely going to be testing."
"Everybody talks about the size of the grounds being a little smaller. They talk about the heat and the dew at night having an effect. It will be a great occasion."
Atletico Madrid kept their La Liga title hopes alive with victory over Gary Neville's Valencia.
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Hampshire captain James Vince says the ICC World Twenty20 can help put him on the path to playing Test cricket.