Middlesbrough - winless in 13 matches - are second from bottom and seven points adrift of Hull.
Middlesbrough's Marten De Roon got one back just before half time, but Harry Maguire headed Hull's fourth midway through the second period.
The hosts sent their supporters into raptures just after the half-hour mark as Hernandez finished off a free flowing passing move to make it 3-1.
Considering the mess Hull were in when Marco Silva arrived in January - for a start, they were six points behind Boro at the time - this is a remarkable turnaround.
Silva, whose unbeaten home record spans spells at Sporting Lisbon and Olympiacos before his arrival at Hull, said another three points on the back of Saturday's win against West Ham outweighed the significance of climbing clear of the bottom three.
Boro's head coach Steve Agnew, still chasing his first win in charge after taking over from the sacked Aitor Karanka three games ago, had urged his side to take the game to their opponents at the KCOM.
Negredo played a fine ball to find Adama Traore, whose shot-turned-cross was met at the far post by the Spaniard with a sliding finish back across goal.
Seth Lugo: Lugo (elbow) having medicals reviewed Tue
Lugo made three appearances in the WBC for Team Puerto Rico and even started in the championship game against the United States. He logged another 11.1 frames for the Mets in Spring Training , managing a 5.56 ERA and 1.50 WHIP.
Middlesbrough looked to respond with the pace of Traore causing problems and Eldin Jakupovic had to be alert when the 'Boro man crossed for Negredo, who saw his first time effort saved by the keeper.
Those same Teesside voices, though, were soon silenced by three goals in 19 minutes from the home side.
It was proper end-to-end stuff and Middlesbrough were nearly back within a goal when Rudy Gestede got up high to meet a deep cross and saw his header tipped onto the crossbar by Jakupovic.
A touchline conflab between Michael Oliver and his linesman gave Hull hope that justice would be done, but the goal stood despite replays clearly showing the Dutch defender had been two yards offside when Gibson headed the ball in his direction.
Middlesbrough reduced the deficit in first-half stoppage time in controversial circumstances.
The icing on Hull's night then came via that late flurry of Spurs goals in south Wales.
Hull City: Jakupovic; Elmohamady, Maguire (Dawson 80), Ranocchia, Robertson; Markovic, Clucas, N'Diaye, Grosicki (Henriksen 88); Niasse, Hernandez (Evandro 50).