Centre-half Maghoma rose to head in Grant Ward's first half free-kick and later made a vital block in the penalty box to thwart the Cottagers before Harrison swept home in stoppage time at the end of the game to seal the win.
There were returns for Ward and Shaq Coulthirst following successful loan spells at Coventry and York respectively as Ugo Ehiogu’s side looked to finish with a flourish at White Hart Lane in the Under-21s' final home fixture of the season.
We almost got off to the perfect start when Nathan Oduwa tied his defender in knots on the left before unleashing a shot that was parried by Cottagers goalkeeper Marek Rodak into the path of Kenny McEvoy but, leaning back, he lifted his shot over the bar.
Kyle Walker-Peters was next to go close as he rolled in off the right flank before fizzing a shot over the top.
We produced some scintillating pass and move football in the Cottagers’ half but our opener was notable for its simplicity. Walker-Peters won a free-kick on the right with one of his weaving runs and Ward stepped up to take it. The delivery was a dangerous one and Maghoma was on hand to plant a header into the far corner.
Ward and Harry Winks provided the creative platform for wave after wave of attack as Fulham were restricted to the occasional counter which Milos Veljkovic and Maghoma mopped up with relative ease.
Coulthirst almost made it two as the half ticked on but despite our dominance, the visitors should have gone in level at the interval.
A long clearance split our defence and allowed Adam Taggart to run through on goal. His composure evaded him at the key moment though as, with just goalkeeper Luke McGee to beat, he dragged his effort tamely wide.
The second half began in the same manner as the first with Fulham pushed back deep inside their own half. Oduwa went close to putting the game to bed when he rattled the crossbar with a curling effort from outside of the box but still the second goal evaded us.
As we hit the hour mark Coulthirst had his first clear-cut opening when Josh Onomah slipped him in but Rodak did well to stand up and thump his effort away.
We survived another scare as Fulham should have levelled with their first attack of note in the half in the 68th minute. This time substitute Luca De La Torre got behind the back four but, like Taggart before him, he dragged wide.
Ange-Freddy Plumain was next to go close for the visitors when he latched onto a long diagonal ball and was thwarted only by McGee, who did well to spread himself in front of the Fulham winger.
The Cottagers smelled blood and when McGee spilled the ball shortly afterwards, an old fashioned scramble ensued before Maghoma eventually threw himself in front of Solomon Sambou’s effort to concede a corner.
The game petered out as time ticked away and the rain started to fall but in injury time we at long last put the match to bed. The lively Winks picked out Will Miller who committed Rodak before squaring for fellow substitute Shayon Harrison to roll the ball into an empty net.
Spurs: McGee, Walker-Peters, Ogilvie, Ward, Veljkovic, Maghoma, McEvoy (Harrison, 62), Winks (c), Coulthirst (Miller, 80), Onomah, Oduwa (Lesniak, 90). Substitutes (not used): McEneff, Miles (GK).
Fulham: Rodak, Baba, Evans, O’Halloran (De La Torre, 54), Buatu (c), Donnelly, Na Bangna, Christensen (Sambou, 45), Taggart, Hyndman, Plumain. Substitutes (not used): Redford, Norman (GK).
Goals: Spurs - Maghoma (16), Harrison (90+4).