The Blues were 32 points down early in the third quarter and seemingly gone after a horror second period, in which they gave away three goals directly from 50m penalties.
But they stormed back to win 18.8 (116) to 14.12 (96) in front of a pro-Richmond crowd of 94,690, bringing a bitter end to the Tigers' first finals campaign in 12 years.
It sets up a semi-final meeting with Sydney at ANZ Stadium on Saturday night.
Judd, whose own season appeared over when he injured his knee a month ago, picked up 11 disposals in the third quarter as the Blues continually won the ball from the stoppages to pile on five goals in an eight-and-a-half minute burst to cut the deficit to one point.
It was out to four points again at the last change.
Carlton's Mitch Robinson appeared set to be the villain when he gave away a free kick in the goalsquare, for thumping the ball straight over the line from a ball-up, to hand Richmond's Ivan Maric an easy goal and the Tigers a nine-point lead.
But it halted the Blues' charge only momentarily.
Eddie Betts (three goals) goaled before Robinson made up for his earlier blunder with a mark and goal to put Carlton in front for the first time since midway through the first term.
Judd then fittingly stretched the margin with a classy goal of his own.
Maric, one of the Tigers' best, answered with a clever snap, but Jarrad Waite and makeshift forward Nick Duigan, a late inclusion, responded by each kicking their fourth majors to stretch the lead to 16 points early in time-on and the Blues were pretty much home.
It was another remarkable recovery for Carlton, who were mathematically out of finals contention before Essendon were disqualified in the lead-up to round 23.
They then went to the verge of losing eighth spot when they were 39 points down against Port Adelaide last weekend, before charging home to win by a point.
It ensured they became the first team to benefit from a rival being kicked out of the finals.
Along with Judd, midfielders Gibbs and Marc Murphy were superb for Carlton, while captain Trent Cotchin was Richmond's best.
CARLTON 2.3 6.5 12.6 18.8 (116)
RICHMOND 3.5 10.7 12.10 14.12 (96)
Goals: Carlton - Waite, Duigan 4; Betts 3; Garlett, Robinson 2; Judd, Scotland, Warnock. Richmond - Edwards, Maric, Cotchin, Vickery 2; Ellis, Newman, Martin, Riewoldt, Petterd, Tuck.
Best: Carlton - Judd, Gibbs, Murphy, Waite, Betts, Duigan. Richmond - Cotchin, Maric, Deledio, Martin, Vlastuin, Tuck.
Umpires: Simon Meredith, Mathew Nicholls, Luke Farmer.
Official Crowd: 94,690 at MCG.