Honours are even heading into next week's quarter-final second leg in Munich after United held the defending champions to a 1-1 draw at Old Trafford.
Without the services of first-team regulars Robin van Persie (injured), Patrice Evra (suspended) and Rafael (injured), United were always facing an uphill battle against Bayern's possession-based game, but David Moyes' men frustrated their German opponents and could have easily taken a lead to Allianz Arena.
And Vidic, who opened the scoring for United, believes the pace of Danny Welbeck and Wayne Rooney can lead the club to their first semi-final appearance since the 2010-11 season, when they dismantled Schalke before being outclassed by Barcelona in the final at Wembley.
"It was a tough game and a good result – and I think it will be the same game next week," Vidic told Sky Sports.
"They will have the same possession, especially as it's their own ground, but if we keep the shape we can hurt them with our pace.
"We felt we had good positions and were solid, but one mistake was punished and they showed what a good team they are.
"They had a lot of possession but we accepted they would and we tried to counter attack."
Meanwhile, United team-mate Alexander Buttner echoed his skippers' confidence, though the Premier League giants have never beaten Bayern in Munich in three previous attempts.
"Of course we can do it, we always believe in ourselves," said Buttner, who replaced suspended Frenchman Evra at left back.
"We had chances to score more goals and we have to focus on that. In defence we did well and we didn't give a lot away – just the goal. I think we have a good chance."
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