United captain Vidic opened the scoring with a header after 31 pulsating minutes before Nani reacted quickest to some goalmouth confusion to prod home five minutes from time.
Spurs were furious with referee Mark Clattenburg for allowing the second goal, scored after goalkeeper Heurelho Gomes placed what he believed to be a dead ball.
Rafael van der Vaart could have put Spurs in front when he curled against the far post and Spurs continued to push.
After Van der Vaart failed to beat Edwin Van der Sar from a tight angle, Roman Pavlyuchenko almost got lucky when his 25-yard effort nearly found its way over the line courtesy of Vidic's deflection. But United held firm in controversial fashion.
Source: PA