Derby have jumped above Millwall into sixth position in the Championship table, while second-placed Cardiff sit just one point above third-placed Fulham with two matches of the campaign left to play.
The away side's first chance of the night arrived in the 23rd minute when Junior Hoilett tried his luck with a first-time volley, but the ball flew over the crossbar.
Cardiff were ahead in the 28th minute, however, when Paterson expertly found the back of the net with a volley that flew into the bottom corner.
Andreas Weimann looked to strike back for the home side in the 37th minute, but the attacker missed the target, before Jamie Ward fired over the crossbar down the other end in the final action of the first period.
Derby started the second period on the front foot, but aside from a Lawrence free kick - which smashed into the Cardiff wall - the home side were finding it difficult to cause Cardiff problems.
Curtis Davies headed over the Cardiff crossbar in the 66th minute as Derby continued to press, and the Rams eventually levelled the scores three minutes later when Jerome poked home from close range following a corner.
Derby then completed the turnaround in the 82nd minute when Vydra struck home from inside the box following smart work from Andre Wisdom.
Yanic Wildschut was at fault for the home side's second, but the Cardiff midfielder almost atoned for his error in the latter stages when he found space in a dangerous position, but he fired wide from an acute angle.
Derby made sure of all the points in the 90th minute, however, when Jerome took advantage of some poor marking from Cardiff defender Sean Morrison to beat Etheridge from close range.
Cardiff are still in charge of their own destiny when it comes to securing automatic promotion, but Fulham have been handed a huge lifeline ahead of their final two matches against Sunderland and Birmingham City.
DERBY (3-4-3): Carson; Forsyth, Davies, Keogh; Olsson (Vydra 60'), Johnson, Huddlestone, Wisdom; Lawrence (Hanson 88'), Jerome, Weimann (Pearce 87')
CARDIFF (4-3-3): Etheridge; Manga, Morrison, Bamba, Bennett; Paterson, Gunnarsson, Ralls; Hoilett (Pilkington 75'), Madine (Zohore 68'), Ward (Wildschut 75')