With the win, Atletico regained top spot in the Primera Division standings as well.
Iker Muniain put the Basques ahead with just five minutes played but Diego Costa pulled Simeone's side level midway through the first half, and Koke dived in to head in the winner in the second half. The hosts finished the game with 10 men when Aymeric Laporte was sent off late on.
Having been temporarily dislodged from the summit by Barcelona's earlier 1-0 triumph at Espanyol, the win got Los Rojiblancos back two points clear of Gerardo Martino's men and left Simeone purring.
"We are aware of our great match," the Argentinian said on clubatleticodemadrid.com.
"It was one of the best in La Liga. We recovered the ball very clearly and were also clear in taking advantage of the gaps for Diego.
"We always knew how to play, we were always strong.
"The team overcame the adversity, from the game, from the commitment and from the intensity, to win a great match.
"The three points are very good in a difficult stadium, with extraordinary fans - a stadium of pure football. It was a very positive match and a great joy because of the result."
Simeone was full of praise for Diego Costa, not only for his equaliser but for the impact he has on his colleagues.
"He's a guy who keeps growing day by day," the coach said. "He has an enormous physical strength. He infects his team-mates with this thing he has and they exploit it in the best possible way."
Simeone said his team would not be overawed by their lofty position ahead of Barca and Real Madrid, and vowed they would continue in the same vein for their remaining fixtures.
"We enjoy this situation day by day, minute by minute, training by training, match by match," he said. "That's where we feel strong and we'll stay that way because we can't leave this line of action."