The Rams are the first side to win at the LD Nutrition Stadium this season, ending a run of three-straight home wins for Ryan Carr's side.
The away side took the lead three times, with a try from former Rovers man Sam Day putting the game beyond the hosts with just over 10 minutes to go.
Dewsbury got off to a flying start and grabbed the game's first points with a well-worked try.
The Rams were the better side for the majority of the first half and deservedly led at the break.
Featherstone struggled to find much rhythm going forward, apart from a five-minute spell when they posted two tries to keep themselves in the contest.
The hosts took brief control in the second half after Dewsbury had opened up a 10-point lead.
But the Rams refused to give in and took the lead for the third time and restricted Rovers' go forward to claim the two points.
The opener came when Paul Sykes floated a short kick into space and Liam Finn was on hand to pluck the ball out of the air and score by the posts.
The visitors weren't ahead for long, though, as Luke Briscoe scored his 53rd Rovers try after taking a great pass from Ashton Golding.
Cameron King then burrowed over from dummy half in trademark fashion to put the home side in front.
Dewsbury eased the pressure on their own line as Robbie Ward broke from inside his own 20.
He combined with Luke Hooley to get within 10 metres of the hosts' line, allowing Dale Morton to dive over the whitewash on the next play.
The away side regained the lead as they moved the ball swiftly to the left with Adam Ryder sending Morton diving over for his second.
Dewsbury finished where they left off at the beginning of the second half as Sykes popped the ball to Samuel Kibula who crashed over from close range.
Sykes added the conversion to give the away side a surprise 10-point advantage.
Featherstone responded as Ben Reynolds found Golding who nipped through a gap to dot the ball down.
Reynolds was at the heart of everything good for Featherstone and put his side in front for a second time as he crashed through three players to score under the posts.
Sykes was sin-binned by referee Gareth Hewer for dissent in the aftermath of the try.
Despite being a man light, Dewsbury scored twice to take the lead, one which they wouldn't relinquish.
Former Featherstone forward Michael Knowles squeezed over in the corner, with Finn adding a brilliant touchline conversion.
Day then put the game beyond the home side as he powered over underneath the posts.
The final 10 minutes of games have proved the Rams' undoing this year but Greenwood's men remained composed to secure their second win of the season.
Tempers flared as the final hooter sounded but the referee opted to keep his cards in his pocket as the players cooled down and shook hands.
Featherstone Rovers: Golding, Briscoe, Hardcastle, Newman, McDaniel, Reynolds, Boas, Wheeldon, King, Smith, Davies, Harrison, Lockwood. Subs: Cooper, Day, Ormondroyd, Makatoa.
Dewsbury Rams: Hooley, Worrincy, Walshaw, Ryder, Morton, Sykes, Finn, Annakin, Ward, Trout, Kibula, Knowles, Igbinedion. Subs: Day, Harrison, Sheriffe, Andrade.
Referee: Gareth Hewer