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Scores from Danny Houghton, Scott Taylor, Gareth Ellis and Jamie Shaul established Hull's first-half cushion.
Luke Walsh reduced Saints' deficit after the break to add to Mark Percival and Louie McCarthy-Scarsbrook's tries.
However, the visitors pulled clear with Curtis Naughton, Kirk Yeaman, Scott Taylor and Fetuli Talanoa scores.
Marc Sneyd was on target with 15 points from the boot.
Saints have a remarkable record when the year ends in six, winning in five of the past six decades, but that quirk was not to be continued as Hull continued their dual push for honours in 2016.
The home side reached the semi-finals last season but failed to match Hull throughout.
Ruck-speed, powerful forwards, ruthlessness with field position and the accuracy of Sneyd's kicking helped the Airlie Birds to dominate the game for large periods, despite conceding the opening tries of each half.
St Helens captain Jon Wilkin told BBC Sport:
"Hull outperformed us in most facets of the game, it's disappointing, it's a big game and we haven't produced.
"You can win game without possession, and whatever through penalties, poor kicking, ill-discipline or dropped-ball we gifted them.
"I thought we were terrible from the start today and without being cynical about the performance, we talked a good game all week and we haven't delivered."
Hull FC head coach Lee Radford told BBC Sport:
"It was massive effort, the conditions, the heat played a major factor but we completed at a high really high percentage which is something we've done all year so long may that continue.
"The boys did good, we made the boys [Frank Pritchard and Sika Manu - away on international duty] a promise we'd be in the draw and they've come good on that promise.
"Marc Sneyd's been fantastic over the past six games, he's leading us around the park really well and he's got one of the best kicking games in the competition.
"For a club of our size and history not to have won at Wembley is a bitter pill to swallow, but we're through and we look forward to whoever we come up against."
St Helens: Lomax; Dawson, Peyroux, Percival, Owens; Fages, Walsh; Walmsley, Roby, Amor, Vea, Greenwood, Wilkin.
Replacements: McCarthy-Scarsbrook, Tasi, Richards, Knowles.
Hull FC: Shaul; Naughton, Fonua, Yeaman, Talanoa; Pryce, Sneyd; Taylor, Houghton, Watts, Washbrook, Minichiello, Ellis.
Replacements: Green, Thompson, Hadley, Bowden.
Referee: Richard Silverwood
Hull FC recorded their first Challenge Cup victory at St Helens since 1926, reaching the quarter-finals with a 47-18 success at Langtree Park.