The home side played much of the game with only one healthy interchange player after Joe Tapine (ankle), Ryan James and Sebastian Kris (both head injury assessments) were ruled out.
And they still found some energy to try to steal the victory when Jordan Rapana was stretching out for the corner with only seconds left on the clock. Tuivasa-Sheck's reach was that little bit longer, knocking the ball from the winger's grasp.
Three minutes earlier and Warriors centre Adam Pompey had put the Warriors in front with their fifth second-half try to claw back the Raiders' 19-point half-time lead.
Earlier, Canberra's Dally M medallist Jack Wighton lifted spirits with a fend and some acceleration, to level scores 6-6 after Warriors prop Addin Fonua-Blake had scored after five minutes in his 100th NRL game.
Then the floodgates opened and Canberra's horror run turned into a dream one.
Three tries came within 10 minutes - to Ryan Sutton, Iosia Soliola and George Williams - all converted by Jarrod Croker who was making his first appearance for 2021 after a shoulder injury.
The half-time score of 25-6 - after a Williams field goal - didn't reflect the dramas the Raiders had to negotiate. But it didn't end there with Croker dislocating a finger and Curtis Scott carrying a rib injury. Both remained on the field.
However, the Warriors rebounded and whittled down that 19-point Raiders lead with five second-half tries.
Kodi Nikorima, who kicked five conversions, sparked the second-half comeback with his 42nd minute try.
Bayley Sironen, Ben Murdoch-Masila and Roger Tuivasa-Sheck scored to narrow the gap before Pompey's 77th minute try gave the Warriors the lead.