Sanchez scored his first goal since January as the two-time defending Copa America champions beat Japan 4-0 in Sao Paulo on Monday.
The Manchester United attacker headed in a cross from Charles Aranguiz in the 82nd minute before setting up Eduardo Vargas a minute later.
Vargas provided a brace for the two-time defending Copa America champions, making him Chile's all-time leading scorer in the competition and the active player with the most career Copa America goals.
Vidal said the goal was just what Sanchez, who netted twice in 27 games for United in 2018-19, needed as he looks to regain confidence following a trying club campaign with the Red Devils.
"Alexis needed the goal. He had a difficult year and this gives him confidence," the Barcelona midfielder said of his long-time team-mate.
Sanchez has helped lead Chile to two consecutive Copa America titles via two consecutive victories over Lionel Messi's Argentina in the tournament finales.
Chile had never won the tournament prior to those two title wins, having finished as a runner-up four times prior to their initial 2015 triumph.
The 30-year-old Sanchez, Chile's all-time leading scorer, has earned 125 total caps for his national team, scoring 42 goals during his senior international career.
However, the Chilean star has struggled since making the move from Arsenal to Manchester United in January 2018, having scored only five goals in 45 appearances for the Red Devils.
Those struggles have seen him linked with a move away from Old Trafford , although a transfer could be difficult given the former Arsenal star's massive wages at Manchester United.
The pair of late goals scored by Sanchez and Vargas wrapped up Chile's win after Erick Pulgar's first-half header and Vargas' deflected strike in the 54th minute.
Vidal, whose team face Ecuador in Group C on Friday, urged Chile to continue improving.
"We must focus from now on that game," he said.
"We know that if we keep improving we can be a very dangerous team."
With three points in hand from their first match, Vidal and Chile will face Ecuador and then Uruguay in their final two group stage matches.