It was a familiar story for Wakefield, who competed well in the first half, but faded after the break.
Their cause was not helped by head injuries to Tom Johnstone and Max Jowitt and the loss of Josh Wood with a damaged elbow.,
Catalans will play Swinton Lions or Warrington in the quarter-finals, when Castleford Tigers face Salford Red Devils.
The rest of the quarter-final; draw was Featherstone Rovers or Hull v Wigan Warriors and St Helens v Leigh or Huddersfield Giants.
Catalans scored 18 unanswered points after leading only 8-6 at the interval.
Trinity thought they had opened the scoring when Mason Lino chipped ahead, regathered and offloaded as he was pulled down just short of the line. Jay Pitts touched down, but video referee Robert Hicks said no try.
Catalans broke the deadlock soon afterwards through in-form full-back Sam Tomkins, who stepped and then stretched over for a try which James Maloney improved.
Wakefield got back on level terms after 26 minutes with a brilliant, improvised touchdown. Tom Johnstone, hemmed in on the left touchline, kicked infield, Lino chased, the bounce was kind and he gathered for a try which he also improved.
Dragons, though, went in at the break with a narrow lead after Joe Westerman went high on Jasson Baitieri and Maloney took the two.
Ten minutes into the second half, Lino kicked out on the full and in the wrestling set Josh Drinkwater dummied over for Dragon’s second try, which Maloney improved.
Mike McMeeken, the former Castleford Tigers forward, was denied a try by video official Hicks with 20 minutes left, after he touched down from Maloney’s cross kick.
But it was only a brief reprieve as Dragons took a stranglehold on the game three minutes later when Tom Davies went over at the corner from McMeeken’s pass and Maloney’s touchline kick made it 20-6.
Moments later, Gil Dudson crashed between the posts for another converted try and at 26-6, there was no way back for Wakefield.