The Canaries relieved some of the pressure on their boss by picking up three vital points thanks largely to an impressive defensive effort against the Eagles
A first-half goal from Gary Hooper ensured the triumph, with the striker getting on the end of a fine ball from Wes Hoolahan to put his men ahead.
The result also marks Norwich's first clean sheet in four Premier League games - and just their second win in all competitions since the end of September - and Hughton was thrilled to get back on track.
"It is a big win and there is certainly a better feeling going into Wednesday's game at Liverpool," he told BBC Sport. "We just have to make sure we have more of them.
"Tony [Pulis] has set Crystal Palace up to be very difficult to beat and they will cause teams a lot of problems.
"I thought we defended well and restricted them to minimal chances."
The win sees Norwich climb to 14th place in the table, with their next challenge coming away to Brendan Rodgers' side on Wednesday.