Wakefield moved a step closer to securing Super League survival after a confidence-boosting 38-10 win over relegation-rivals Hull KR.
Trinity climbed two points away from the bottom of the table and ended a five-game losing streak with the vital result at KCOM Craven Park.
But relegation worries continue to grow for the Robins as they remain in 11th spot, level on 18 points alongside Huddersfield and London.
Wakefield then took the lead in the 10th minute when Miller dived over for his first score, with Brough adding the extras.
Trinity extended their lead to 8-0 six minutes later through a penalty goal by Brough, before it went from bad to worse for the Robins when Jones-Bishop crossed the whitewash.
The visitors shifted the ball to the right, Reece Lyne slipped out of a tackle and drew the winger to put Jones-Bishop through.
Full-back Adam Quinlan came off with a head knock, which forced the Robins into a reshuffle in their backline.
But the change in personnel did not affect the hosts as Mitch Garbutt used brute strength to power past Wakefield's defence and crash over.
Shaw made no mistake with the conversion as the home side cut the deficit to 14-10 at the break.
Wakefield started the second period with renewed enthusiasm and quickly built on their lead.
Kyle Wood took advantage of a quick play-the-ball to burrow over, which was converted by Brough to increase their advantage to 10 points.
Trinity blew two scoring opportunities as they continued their momentum, which was aided by sloppy ball-handling from Hull KR.
But victory was beyond doubt when Tupou barged over from acting dummy-half, while Miller crossed after collecting off his own grubber kick in the final 16 minutes.
There was still time for Hampshire to touch down twice, firstly pouncing on a loose ball to cross in front of the travelling fans before the winger added gloss to the scoreline by collecting his own chip over the top with three minutes remaining.