After the teams could not be separated in regulation time - with the score locked at 0-0 - penalties determined the winner and it was United who prevailed at FedEx Field.
Captain Darren Fletcher stepped up and converted the winning penalty after Marco Andreolli's effort cannoned off the crossbar.
The result preserved United's perfect record in the United States, with three wins from three.
Manager Louis van Gaal made four changes to the starting XI that took to the field in the 3-2 victory over Roma on Saturday, with Anders Lindegaard, Chris Smalling, Fletcher and Ashley Young returning to the line-up for their reunion with former United captain Nemanja Vidic.
Inter made just one change to the team that beat Real Madrid on penalties in California on Saturday, with Joel Obi dropping out for Rene Krhin.
A number of United youngsters were given game time in Denver but the return of senior personnel was clearly a boost and it showed with the Premier League outfit coming close to breaking the deadlock in the 10th minute.
United defender Phil Jones stooped low to direct his header towards the bottom corner of the net but Inter goalkeeper Samir Handanovic got his hand to the ball and denied Jonny Evans on the rebound in a goal-mouth scramble.
There were few clear-cut chances throughout the first half, though some neat interchange play between Wayne Rooney and Juan Mata almost resulted in the opening goal, but the Inter defence were up to the task.
Wilfred Zaha was the only player in United's travelling squad not to have played a minute prior to Tuesday's clash but he was given time in the second half and came close to netting the opener within minutes of his introduction after a driving run from halfway.
Inter almost won it at the death after being awarded a free-kick, however David de Gea denied Fredy Guarin from 25 yards out as the match headed to penalties.
United would not be denied a third successive victory in the USA, albeit after a shoot-out, and will now turn their attention to Saturday's clash with Real Madrid.
Inter are back in action against Serie A rivals Roma on the same day.
