The former Mexican international striker turned in a remarkable performance Saturday, leading his team to a comeback win.
The Mexican striker opened the scoring with six minutes gone, but the visitors scored three unanswered to make it 3-1 in the 56th minute. However, Vela scored in the 61st, 78th and 81st minute to complete a thrilling turnaround at the Estadio Anoeta.
Sociedad's comeback was sparked by a 65th-minute red card for Celta midfielder Andreu Fontas, who was sent off for two yellow card offenses.
The victory was Sociedad's third straight at home in the league and moves the Basque side up into sixth in the La Liga table.
Entering the match, Vela had gone eight consecutive matches without scoring but after his four strikes, he now has nine goals on the season in all competitions, including six in La Liga play.
Vela has not featured for the Mexican national team since 2011, and has continued to turn down invitations to play for El Tri, which qualified for the World Cup earlier in the week with a 9-3 aggregate victory over New Zealand.