The Black and Whites started the game on fire with a try by Chris Green in the second minute.
The Giants hit back with two close-range scores from Joe Wardle and Ukuma Ta'ai giving them a 12-6 lead, before Kirk Yeaman closed the gap to two points at the break.
Jermaine McGillvary rose above Tom Briscoe to extend the visitors' lead to six after collecting Brough's kick.
A big hit on Luke Robinson by Gareth Ellis helped Hull to level with Mark O'Meley's try. Robinson did not return, but Brough stepped up to give the Giants a late lead with a spectacular try that earned them the two points.
Hull KR recovered from a 12-point half-time deficit to defeat Salford 28-18 and extend their winning streak to five matches.
The hosts looked in real danger of seeing their run of victories come to end after trailing 18-6 at the break but they staged an impressive second-half fightback to take the spoils at New Craven Park.
Cory Paterson, with his second of the match, Michael Dobson, who also kicked four goals, Craig Hall and Travis Burns all went over in the second period to help Rovers secure the two points. Wayne Godwin, Stephen Wild and Matt Ashurst crossed for the visitors.
Winger Tommy Makinson's hat-trick of tries helped St Helens burst Castleford's bubble with a 40-24 win and quell talk of a crisis at Langtree Park.
Saints had been put on a warning by angry chairman Eamonn McManus after last week's home defeat by Hull KR left them in serious danger of missing out on the Super League play-offs for the first time.
Amid sweltering temperatures, the Tigers turned the heat up on their visitors by racing into a 10-0 lead after 18 minutes and the early loss of England hooker James Roby with an ankle injury looked to have compounded their misery. But Nathan Brown's men hit back with Makinson's first try on 22 minutes and he added two more in the second half to clinch an 11th consecutive win over Castleford.