It looked as if Warrington, four-time Challenge Cup winners since 2009, were on course for victory at 6-2 ahead and with time almost up at a rainswept Wembley Stadium.
Davies, however, pounced in the 78th minute as Warrington failed to defend a grubber kick into their in-goal area.
But the wing's try only levelled the scores at 6-6 and it still needed a conversion from Mikey Lewis to seal the win for Hull KR, previously without a major trophy in four decades.
Victory meant the Robins, beaten just once in 13 Super League games so far this season, kept their double hopes alive.
Earlier, Hull KR opened the scoring thanks to a Lewis penalty but Warrington, four-time Challenge Cup winners since 2009, led 6-2 at the break.
Marc Sneyd's high spiral kick was fumbled by Hull KR's Joe Burgess, giving Warrington excellent field position near the posts.
With the final play of the ball in a set of six tackles, Sneyd's grubber kick deflected off the boot of the unlucky Joz Litten and headed towards the right corner, where the unchallenged Josh Thewlis touched down.
Sneyd then made light of a tough conversion with a superb kick and Warrington were four points ahead at half-time.
Hull KR, who last won the Challenge Cup when beating local rivals Hull back in 1980, pressed hard to get back on level terms.
But determined Warrington defence and superb tactical kicking from Sneyd kept them at bay until the 76th minute when Sam Powell came in over the top on Davies to give the Robins a penalty.
Hull KR ran the ball before Tyrone May put in a teasing grubber kick over the try-line.
Aaron Lindop could not get a hand on the ball for Warrington and the onrushing Davies touched down, although it needed the video referee to confirm he had levelled the scores.
Lewis added the conversion and Hull KR were two points ahead at 8-6.