The Manchester United striker opened the scoring with 20 minutes left and he netted again seven minutes from time.
Glasgow Celtic midfielder Graham Carey scored Ireland's second goal on 70 minutes with a long-range effort from 40 yards that squirmed through the 'keeper's hands and Donal McDermott completed the scoring with three minutes left.
The comprehensive win gave Ireland the win they were looking for in the opening match, as well as providing them with a healthy goal difference.
Dubliner Fagan grew up in Church Street in Dublin, barely ten minutes walk from Dalymount Park, and his goal proved to be the lifesaver for Ireland in a match which failed to produce many chances for the sizeable crowd of 2,000.
His first goal arrived after substitute Cillian Sheridan, only on the pitch 60 seconds, burst down the left and crossed for the striker to tuck the ball home from six yards.
Carey secured the points with the second goal and Fagan nodded home the third from Donal McDermott's cross. It was McDermott who crowned a great second half display to make it 4-0 by blasting home from 12 yards.
Romania looked most likely to score in the first half and the Republic were let off lightly on 24 minutes when Jianu fired wide with the goal at his mercy.
Once they achieved the breakthrough, though, Ireland upped their game and they now sit on top of their qualifying group with three points, ahead of Israel on goal difference.
Ireland play Israel on Wednesday at Richmond Park at 7 pm. Serbia & Montenegro play Romania on the same day at UCD grounds, Belfield, at 2.30 pm.
REP OF IRELAND: Shane Redmond (Nottingham Forest), Andrew Callaghan (Millwall), Lorcan Fitzgerald (West Ham) ? Captain, Michael Spillane (Norwich City), Gavin Donoghue (Sunderland), Donal McDermott (Manchester City), Graham Carey (Glasgow Celtic), Paul Cahillane (Glasgow Celtic), Michael Daly (Manchester City), Tom Lyons (Crystal Palace), Christy Fagan (Manchester United).
SUBS: Harry Arter (Charlton Athletic) for Daly - Half-time, Cillian Sheridan (Belvedere) for Lyons - 59 mins. Gary Breen (Manchester City) for Cahillane - 72 mins.
ROMANIA: Cosmin Razvan Ciumna, Ahmet Ferdin, Alexandru Iacob, Alexandru Dresca, George Calintaru, Gabriel Torje, Marian Liviu Militaru, Iulian Razvan Ochirosii, Marius Ioan Feher, Marius Jianu, Tudor Balmos.
REFEREE: V. Aliyev (Azerbaijan)