The La Liga title-chasers were without the suspended Diego Costa for their trip to Vigo after his yellow card for simulation against Real Madrid was not overturned, but ultimately it did not matter as Villa starred.
After a disappointing first half, Atletico eventually started to dominate early in the second period and Villa latched on to Jonny Castro's terrible 62nd-minute backpass before beating Yoel.
The forward's second of the match arrived two minutes later as he converted from Jose Sosa's right-wing cross.
Simeone said: "He (Villa) lives on goals. He is a specialist in that, and the more options you have about the goal, the better for all.
"His accuracy and the strength has marked his career. He has put in such good effort for the team and he is an important player for us.
"We need him. We need his goals, his experience and he is one of the few players who is used to fighting every Sunday for first place (in the table). His forcefulness in the area is worth having."
Villa was understandably content and urged his team-mates to treat their remaining matches as finals as they seek a first league title since the 1995-96 season.
He added: "We are very happy with the victory in a complicated ground against a team which plays high-quality football.
"From now on until the end (of the season) all matches are finals and we must win them all."
