BATE strung some neat passing moves together in the early stages at a damp Mestalla but Valencia looked far more dangerous in attack than the Belarussian champions and took a deserved 26th-minute lead when Jonas bustled through a tackle and volleyed in from close range.
Roberto Soldado made it 2-0 from the penalty spot three minutes later, his fourth goal of the campaign following his treble in the 3-0 win at BATE last month, after Artem Radkov had felled Andres Guardado on the edge of the area.
Fernando Gago's fine assist released Feghouli to make it 3-0 six minutes into the second half before Valencia goalkeeper Vicente Guaita failed to deal with Renan Bressan's inswinging free-kick two minutes later and the ball squirted into the net at his near post.
With the home side cruising, Gago surrendered possession to gift BATE a second goal seven minutes from time but any hopes they had of snatching a point were snuffed out when Feghouli netted his second of the night in the 86th minute.
Substitute Ever Banega floated the ball over the defence to the Algeria midfielder and he took it down before beating Andrei Gorbunov for a second time with a fierce drive.
With four of six matches played, Valencia have nine points, level with Bundesliga side Bayern Munich after last year's runners-up thumped Lille 6-1 in the Bavarian capital. BATE have six in third with Ligue 1 club Lille on zero and already eliminated.
"Getting nine points is key and I'm very happy for my two goals and the team's attitude," Feghouli said in an interview with Spanish television.
"The goal now is to win the next two games and give our fans a victory against a great club like Bayern," added the 22-year-old, who had failed to score in 10 previous appearances in Europe's elite club competition.
PRESSURE EASED
Captain Soldado, whose participation in the match was in doubt after a recent family bereavement, was lucky to be on the pitch to score his penalty after he lashed out with an arm at Maksim Bordachev early in the game.
The match officials took no action and he went on to score his 14th goal in his last 13 Champions League starts.
Valencia's victory will further ease pressure on their Argentine coach Mauricio Pellegrino, who has made an erratic start to his first season in charge.
A former Valencia player who worked as an assistant at Liverpool and Inter Milan under Rafael Benitez, Pellegrino came under fire after his side took only five points from their opening five La Liga matches.
The 2000 and 2001 runners-up have a chance to seal their passage to the knockout round when they host Bayern, who beat them on penalties in the 2001 final, on November 20 before they play their final game at Lille on December 5.
"Up until we went 3-0 ahead we projected an image of solidity," Pellegrino told a news conference. "The game against Bayern will be decisive."
BATE, meanwhile, continued their poor form away from home in the Champions League. They have won only one of their eight matches on the road, losing four
