Making his second league appearance since joining from lower division side Derby County on loan deal during the transfer window, Grant made a string of saves to help Stoke secure a point against Jose Mourinho's side.
The 33-year-old has proven to be an adequate replacement for Jack Butland, who is out with an ankle injury.
"Lee was great again today, and when you come to places like Old Trafford you need everybody to play well, not least your goalkeeper," Hughes told the club website(www.stokecityfc.com).
"You need your 'keeper to make match-defining saves and protect your position to help you stay in the game."
Stoke have conceded 16 goals this season and have the worst goal difference in the top flight, but Grant stood out at Old Trafford.
"We have struggled in that regard this season I have to say, but Lee has come in to good effect, he is a good guy and he has a lot of experience - maybe we underestimate how much experience he actually has," Hughes added.
"He is enjoying his time here, getting opportunities that maybe he didn't think he would have and he is taking them chances with both hands."
Stoke, who are second last in the league standings, host bottom-placed Sunderland on Oct. 15.
