Their supporters chanted "City are staying up", and although safety is not certain, it felt like a defining moment at the foot of the Premier League, more so in the case of Agnew's team, ...
"But we didnt do enough second half and we conceded a soft goal from our point of view".
Victory was the Tigers' fifth in six home league games and lifted them two points above Swansea, while Boro, without a league win since December 17, appear destined for a return to the Sky Bet Championship.
Marco Silva's side trailed to Alvaro Negredo's opener, but Lazar Markovic equalised before Oumar Niasse and Abel Hernandez put Hull in control at the KCOM Stadium.
Boro, who have taken one point from three games since sacking Aitor Karanka last month, were backed by 2,500 travelling fans at the KCOM, where Agnew spent over two years as assistant boss to Steve Bruce.
"The teams all around us are going to be playing each other, so I'm thinking maybe 38 or 39 points is what we need". They scored the first time they attacked but we responded very well.
Maguire had a huge hand in Hull's third goal, converted by Abel Hernandez, but Middlesbrough pulled one back before half-time, though Marten de Roon's effort should have been disallowed for offside.
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Those same Teesside voices, though, were soon silenced by three goals in 19 minutes from the home side.
Ben Gibson failed to deal with a deflected looping cross from Andrew Robertson and Markovic took advantage to toe-poke home from close range.
The end-to-end stuff continued unabated as a Middlesbrough surged forward, Rudy Gestede's goalbound header being tipped onto the bar by Hull 'keeper Eldin Jakupovic.
Boro reduced the deficit in first-half stoppage time in controversial circumstances.
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.
Alfred N'Diaye brought a smart save from Valdes, then both Robertson and Grosicki were unfortunate to see inviting crosses go begging.
The icing on Hull's night then came via that late flurry of Spurs goals in south Wales.
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