The visitors took the lead on 47 minutes and, despite several clear-cut efforts on goal, Colin Calderwood's side could not find an equaliser.
After a cagey opening, Spurs were awarded a free-kick in a threatening position which was taken by Clemence. The first to react was Rebrov with a snappy downward header that Herrera in the Fulham goal did well to save.
It was fairly uninspiring fare in the shivering cold of Stevenage and chances were few and far between in the first half.
One promising moment came when Rebrov dispatched a teasing crossball that evaded the defender and Ferdinand pounced only for Herrera to stand firm and collect.
Gary Doherty was replaced by Paul O'Donoghue after 30 minutes, although it was not clear whether the Irishman was injured.
Fulham pressed just before the break and a cross by John Collins was met by Stuart Nobel and his low snapshot was saved well by Hirschfeld.
Spurs responded and a long clearance was flicked on by Ferdinand and Rebrov worked himself a yard of space before firing over from just inside the area.
Just after half-time Fulham took the lead when a Dean Marney slip to the right of our penalty area let in Sean Doherty for a clear shot on goal. The midfielder advanced and planted his shot beyond Hirschfeld and into the bottom left hand corner.
Fulham nearly increased their advantage when a Malik Buari corner was met unchallenged by Zesh Rehman, but his header went just wide.
Marney caused havoc at the right end on 53 minutes when he burst down the right flank and his cross-shot was clawed out from under the bar by Herrera. Rebrov then had a clear chance to level when put in the clear by Taricco, but lobbed his effort onto the roof of the net.
Ferdinand was again unfortunate not to score on 80 minutes when a Ricketts cross cleared keeper, but his header was cleared off the line by the alert Robert Watkins.
Mark Hughes replaced Jonathan Blondel just after the hour mark as Spurs attempted to establish a stronger presence in central midfield.
Ferdinand nearly levelled the score when, from a long ball from Ronnie Henry, Herrera charged off his line to challenge the striker and came off second best. Unfortunately the ball ran past the post from his header. Clemence then had a shot parried by Herrera after a neat interchange with Ricketts.
Taricco was next to try his luck with a powerful drive just a few minutes from the end, but Herrera was equal to it and managed to tip it over.
There was a great urgency about the Spurs play in the closing stages and the young Fulham side can take credit for withstanding the fairly constant pressure.
Team: Hirschfeld, Marney, Thatcher, Taricco, Henry, Doherty (O'Donoghue 30), Clemence, Ricketts, Blondel (Hughes 61), Ferdinand, Rebrov. Subs: Sutton, Burch, Galbraith.
Fulham: Herrera, Rehman, Green, Watkins, Hudson, Collins, Buari, Shevel, Nobel, Cornwall, Doherty. Subs: Fazakerley, Flitney, Pratley, Lock, Stratford.
A lively young Fulham team denied our reserve side with a resolute rearguard action at Stevenage on Monday evening.