Vaughan, who is on loan from Norwich, scored a hat-trick at Ashton Gate to boost Huddersfield's chances of avoiding the drop to League One.
Robins said: "James showed how much he cares about our club with the way he celebrated his goals. That isn't always the case with loan signings.
"He has been good for us and I think we have been good for him. What the future holds I can't say, but he was terrific today.
"It's amazing to be on 57 points in the Championship and not be mathematically safe.
"The support from our fans was magnificent and we now have the opportunity to finish our season with a good home display against Barnsley next Saturday."