Paul Doolin scored a timely first goal of the season to put Shelbourne safely through to the third round of the cup and end St Francis's faint hopes of an upset.
Doolin was left unmarked at the back post on 67th minutes to head home Carel van der Velden's crisply struck corner, despite the best efforts of Cathal Warfield to keep it out. The irony of the goal for St Francis was that the corner had been needlessly conceded by full back Brian Rickard.
Having got their noses in front, injury-hit Shelbourne threatened to run riot with Warfield coming into his own to keep the scoreline down in the final 20 minutes.
He made a brilliant stop to deprive Dessie Baker within a minute of St Francis falling behind and then made two spectacular stops from van der Velden and Pat Fenlon as Shelbourne hunted for further goals to kill off the scarcely disgraced First Division side.
Playing into the strong wind in the first half didn't hinder Shelbourne who started without influential striker Stephen Geoghegan through injury and James Keddy because of flu, and they wasted a glorious chance after just 35 seconds.
Fenlon's corner was met by captain Pat Scully whose header flew just wide of Warfield's lefthand post.
Another opening, created by Owen Heary's surging run up the right onto van der Velden's ball, went abegging minutes later with Dessie Baker's flick not coming off and Tommy Byrne's shot being smothered by two defenders.
Van der Velden was narrowly wide with a curling right-foot shot on 12 minutes before St Franics settled down to hold their own until the break, creating two reasonable chances in the process.
The first, on 33 minutes, came about when Richie Baker was dispossessed by Micky Gahan who got forward to shoot into the sidenetting.
Four minutes later Gavin Moore's ball into the area forced Steve Williams into an awkward save from Gavin Doyle.
With the win at the backs in the second half, Shelbourne gradually turned the screw on a gallant St Francis and in truth were far better value for their win than the narrow scoreline would suggest.
Paul Gascoigne will make a comeback in a friendly against Shelbourne on Monday night.
The 32-year-old Middlesbrough midfielder, who last played in the English club's FA Cup defeat at Wrexham, has recovered from a knee operation and will play, according to boss Bryan Robson.
Robson said: "I want a serious work-out, and Gazza should benefit from the game. He will return to the side along with Gary Pallister, who has recovered from a back problem. The game will come too soon, however, for Paul Ince, Colin Cooper, and Keith O'Neill."
Gascoigne spent the New Year at a health farm in a bid to boost his fitness. He missed out on the festive celebrations and even trained alone on New Year's Day.
Robson will send a strong squad to Dublin to give his firstteam players valuable match practice during an 18-day break forced upon them by Manchester United's World Club Championship commitments in Brazil and their early exit from the FA Cup.
ST FRANCIS: Warfield; Saul, Heavey, Murphy, Rickard; Peters, O'Sullivan, Murray, Gahan; Doyle, Moore. Subs: Scott for Murphy (75 mins), Keegan for O'Sullivan (80 mins), Lawson for Doyle (89 mins).
SHELBOURNE: Williams; Heary, Scully, McCarthy, D Geoghegan; R Baker, Doolin, Fenlon, van der Velden, Byrne; D Baker. Subs: Kelly for Doolin (78 mins), Campbell for Byrne (84 mins).
Referee: J McDermott (Dublin)
