Manager Oscar Garcia made seven team changes with Tuesday's important Championship clash at Burnley in mind, but his squad players responded with an impressive display to win 3-1 in the Vale Park mud.
But Solomon March put Brighton back in front just before the interval and the gulf in class was apparent in the second period.
The away side went close on several occasions before Jon Obika, on loan from Tottenham, poached a killer third goal 12 minutes from time.
Jones said: "We are very pleased with what the players have given us. The attitude of all of them was spot-on in difficult conditions.
"We made changes but the players are in the squad for a reason. We are fortunate to have strong competition for places and all the lads who came in have performed well.
"I don't really want to single out anyone, but Matt Upson was magnificent and led by example. He's 34, he's played for England, but his hunger and desire are still there for all to see.
"I thought Jon Obika should have scored before he finally did. He's usually a clinical finisher but he failed with one chance before putting that one away in style.
"Jon plays on the shoulder of the last defender and having him here gives us very good options up front.
"As a club we are delighted to be in the last 16. Brighton have got a very good FA Cup tradition and there is a buzz around the players in the dressing room."