Hugill gives Cardiff finale win over Derby
Last updated on .From the section Championship
Cardiff went ahead with their first shot on target of the match, with Eli King holding the ball up in the Derby box before playing in Hugill to score.
Louie Sibley came closest to drawing Derby level, but he shot just over.
Defeat rounds off what has been a difficult time for Derby, the club's administration and historical financial breaches resulting in a 21-point deduction this campaign.
Wayne Rooney's side battled hard throughout the campaign and would have comfortably stayed up if not for the points deduction, but ultimately they find themselves playing in League One next season.
Victory, a first in six games for Cardiff, sees them finish the season in 18th, 16 points clear of the bottom three.
Finishing well clear of the relegation zone was far from a certainty for a long period of the season, but Steve Morison has successfully steered the Bluebirds away from trouble.
Derby were one of only five teams to score less goals than Cardiff this season, so it is no surprise it took 36 minutes for the game's first shot on target.
Liam Thompson was first to force a save from Dillon Phillips, before the Cardiff keeper was called on again to push behind Lawrence's curling effort.
Sibley almost scrambled in the resulting corner at the back post, but last-ditch defending denied the hosts who were finally in the ascendency.
Hugill was brought down in the Derby area as the first half drew to a close, but Cardiff appeals fell on deaf ears, and Lawrence almost broke the deadlock at the other end only to be denied by the woodwork.
The second half started much like the first, but 10 minutes in the Bluebirds had their goal.
On-loan full-back Cody Drameh - who was voted the club's player of the season despite only joining in January - broke down the right and crossed for King.
The Cardiff youngster held the ball up brilliantly and picked the perfect pass for Hugill to run onto and flick the ball beyond goalkeeper Ryan Allsop.
Steve Morison brought on Issak Davies just after the hour mark, but there were concerns for the Cardiff academy player who was forced off 15 minutes later through injury.
Derby pushed for an equaliser to give their fans something to celebrate and Sibley's excellent turn on the edge of the area opened up a sight of goal, but his shot crept just over.
But it was not to be for Rooney's side and League One awaits after finishing 23rd, seven points from safety.
Cardiff City manager Steve Morison told BBC Sport Wales: "We knew they'd have a lot of the ball, they've done excellent, it was very much like the game against them at our place.
"We frustrated them, didn't give them clear-cut chances, and knew we would grow into the game.
"Ending the season with a win is really really pleasing."