"It was important that the inauguration should begin on a good footing with a victory and I'm absolutely delighted," he said.
Santiago Mina pulled one back for Celta when he angled a back-header over goalkeeper Iago Herrerin's outstretched hands in the 79th.
Celta missed other opportunities. Athletic goalkeeper Iago Herrerin gave away a penalty in the 26th when he brought down Manuel "Nolito" Agudo in the area, but the forward shot over the crossbar.
Dias just missed a second in the 41st when his shot went high after having found himself alone in front of goal after a counterattack.
"I'm focusing on the match. The stadium will likely be here another 100 years, but the three points being battled for today, if lost, won't come back again," said Jose Angel Iribar, 70, who played 614 games for Athletic from 1964-1980 and was watching from the stands.
In another match, Elche was held to a 0-0 draw by visiting Valladolid.
Atletico Madrid and Barcelona lead the standings with 12 points from four games, while Athletic is fifth on nine points and Celta is eighth.