Holt opened the scoring after 11 minutes before Simeon Jackson doubled the Canaries' advantage 12 minutes later, with the home side going on to keep only their third clean sheet of the season.
Norwich boss Paul Lambert named an unchanged line-up, sticking with the same XI that earned an excellent 3-3 draw against Arsenal at the Emirates last Saturday, while Alex McLeish made two changes to the side which drew 1-1 with Tottenham, with Alan Hutton and Charles N'Zogbia replaced by James Collins and Gabriel Agbonlahor.
That point against Spurs effectively secured Aston Villa’s Premier League status for another season, with an all but impossible swing in goal difference required to send McLeish’s side down on the final day.
The Midlands side have endured a terrible campaign, winning only two Premier League games since the turn of the year and the visitors showed no sign of improving upon that record at Carrow Road.
Norwich City dominated from the first whistle and soon took the lead, with Bradley Johnson swinging in a superb cross which Holt put into the back of the net, although replays showed Holt may have used his arm.
That was Holt’s 70th goal for the club, with the 31-year-old becoming only the eighth Norwich player to have reached the milestone.
The hosts continued to dictate the pace of the game against a Villa side disintinctly lacking in motivation and Jonathan Howson nearly made it two after 13 minutes, only to be denied by a superb one-handed save from Shay Given.
It did not take much longer for Norwich to double their lead when Jackson took advantage of some awful defending by Carlos Cuellar to fire home.
Given then produced another smart stop to deny Elliott Bennett as Norwich looked to make it three before the break.
Villa were awful in the first half but emerged from the break with renewed vigour and went close soon after the restart when Emile Heskey fed Stephen Ireland, who saw his shot well saved by John Ruddy.
Ruddy then produced another fine stop to deny Heskey but Norwich soon refound their feet and began to dominate possession as they had in the first half.
Jackson went close to grabbing his second goal of the game when his low shot was kept out by a superb diving save by Given, while Bennett then fired narrowly over after waltzing into the penalty area.
With the three points secure, Norwich were happy to play possession football and Villa, who finish the season in 16th, had given up the ghost, although Barry Bannan fired a long-range shot just over the crossbar in stoppage time.