John Doyle led from the front at Dr Hyde Park as Kildare booked their place in the second round of the Bank of Ireland All-Ireland Football Qualifiers.
There was no repeat of Roscommon's memorable 2003 win over the same opposition as the Lilywhites survived eight minutes of stoppage time to progress.
Doyle struck 1-08 in all with Mark Hogarty setting up his goal just before the break.
The Rossies trailed by 1-08 to 0-08 at half-time and while Karol Mannion's 47th minute goal saw the hosts go in front, a Padraig O'Neill goal, allied to Doyle's assured finishing, ensured Kildare's advance to the second round.
Allenwood ace Doyle, who lined out at centre-forward, was certainly Kildare's game-breaker but it was corner-forward O'Neill's 64th minute goal which proved to be the decisive score for John Crofton's men.
The visitors may have played against the wind in the opening half but they led by 0-04 to 0-01 after just nine minutes with Doyle registering three of Kildare's points and Roscommon's lone score coming from their only attack during this period from Cathal Cregg.
With midfielders Seamus O'Neill and Michael Finneran snaffling more and more ball, Roscommon were back on terms by the 17th minutes with Derek Connellan, Ger Heneghan and O'Neill all popping over excellent points.
Playing in towards the town end, Kildare continued to depend on Doyle for scores. His marker John Nolan was struggling to keep tabs on the Lilywhites' leading light but points from Mannion, who fisted over after a Gary Cox set-up, and a subsequent free from Cox shot the Rossies into a 0-06 to 0-05 lead.
O'Neill and Doyle replied though and big full-forward Jason Phillips made it three points in quick succession for Kildare.
Doyle was certainly on fire and he gave Crofton's charges a four-point advantage in the 33rd minute when a fisted pass from Hogarty, who had burst forward from his centre-back berth, led to Kildare's first goal.
Although Kildare had a chance to find the net for a second time just before the interval, thanks to good work from David Lyons, James Kavanagh and Michael Conway, Roscommon right corner-back Sean McDermott came in to avert the danger with a spectacular high catch and clearance.
The Rossies, who brought Enda Kenny on for Cregg at the start of the second half, upped the ante with a quick point from Cox and then Mannion was worked in for his goal.
Cox began the move, feeding the ball to David Keenan, one of the county's All-Ireland winning minors from last year. Keenan found the lurking Mannion and the full-forward's powerful shot was planted to the back of the net.
Kildare replied with gusto, notching three of the next four points as two Doyle points and a brilliant 45-yard effort from defender Emmet Bolton swamped Cox's second point of the half.
Doyle's seventh point of the afternoon levelled the sides at 1-11 apiece and although John Maughan's hosts went ahead soon after, O'Neill's goal, set up by Doyle, came at a perfect time for Kildare - especially as it preceded a poor miss from a free from Cox.
However, the game was far from over and Kildare had to endure eight minutes of stoppage time before confirming their first ever away win in the qualifiers.
They achieved it with two late points - Ken Donnelly and Doyle did the business as Roscommon's challenge petered out with Heneghan grabbing an ultimately meaningless score at the death.
Roscommon: G Claffey; S McDermott, A McDermott, P O Connor; S Daly, J Nolan, R Dooner; S O Neill (0-01), M Finneran; J Tiernan (0-01), G Cox (0-04, 2f), C Cregg (0-01); D Connellan (0-02), K Mannion (1-01), G Heneghan (0-03).
Subs used: S Purcell for O Connor (9 mins), D Keenan for Dooner (30), E Kenny for Cregg (half-time), D Hoey for Tiernan (70).
Kildare: E Murphy; E Callaghan, K O Neill, A McLoughlin; A Rainbow, M Hogarty, E Bolton (0-01); R Sweeney, D Lyons; J Kavanagh, J Doyle (1-08, 5f), K Donnelly (0-01); M Conway, J Phillips (0-01), P O Neill (1-02).
Subs used: T Rossiter for Kavanagh (53 mins), M Foley for Lyons (58), T Archibald for Rossiter (70).
Referee: John Bannon (Longford).