Inspired by half-backs Albery Kelly and Marc Sneyd, Hull scored three tries in quick succession during a devastating 11-minute first-half spell to take a grip on the game.
Centre Carlos Tuimavave scored twice as Hull FC produced the perfect response after conceding more than 50 points in their last two games against Salford Red Devils and Leeds Rhinos.
After the 24-10 Super League success, Radford said: “I thought we did a really good job today.
“We defended well when Leigh had sustained spells of pressure and the win gives us something to build on.
“Our away support was phenomenal throughout the game and gave us lifts when we needed it. That has a huge knock-on effect on the performance.
“The tempo and decision making was better than it has been over the last three or four weeks.”
Radford continued: “I was really pleased with how we performed.
“My confidence as a coach has not been dented one bit in the last few weeks but as a team we looked like we were enjoying defending again.”
Leigh Centurions: McNally, Hampshire, Crooks, Dawson, Thompson, Reynolds, Drinkwater, Green, Hood, Hopkins, Vea, Stewart, Hansen. Substitutes: Higham, Weston, Tickle, Burr.
Hull FC: Shaul, Fonua, Connor, Tuimavave, Michaels, Kelly, Sneyd, Taylor, Washbrook, Watts, Manu, Minichiello, Thompson. Substitutes: Ellis, Fash, Litten, Turgut.
Referee: Gareth Hewer (RFL).