The Brazilian forward, who joined the Primeira Liga champions from Bahia in the close-season, had not scored for Benfica prior to the contest at Estadio do Bonfim.
However, after Eduardo Salvio's superb curling effort had put Benfica ahead, Talisca broke his duck by smashing home from inside the penalty area and duly made it 3-0 with a well-placed free-kick shortly before the break.
Benfica continued to dominate in the second half and Talisca capped a dream evening with a third from close range after Andreas Samaris' initial effort had been saved.
Ola John then rounded off the scoring and a comprehensive win in the 76th minute.
It took just 10 minutes for the visitors to make a breakthrough, Salvio bending a terrific strike into the far corner from the right edge of the area.
Giovani had the ball in the net for the hosts soon after but the whistle had already blown for offside.
Having survived that mini scare, Benfica went 2-0 up in the 38th minute. Vitoria failed to clear a cross from the left and Talisca lashed home a half-volley from eight yards.
Two minutes before the break Benfica essentially made sure of the points, Talisca keeping his free-kick low and finding the bottom-left corner.
His hat-trick was completed 10 minutes after the restart. Lukas Raeder did well to save Samaris' strike from the edge of the box but Talisca was on hand to place home the rebound.
Benfica were not finished there, though, and Lima's fine delivery across the face of goal was met by John at the back post, who could not miss.
