The visitors had to come from behind after going 10-0 down in the first 10 minutes. A try from captain Joe Marler, converted by Freddie Burns, brought England back into the game and Forsyths opening score put them ahead for the first time as he finished off a great break from club colleague Will Hurrell.
Bristol prop Mako Vunipola scored two tries of his own before Forsyth added his second underneath the posts in the second half.
Winger Marcus Watson scored Englands final try, but they would have been disappointed to let Tucuman back into the game with two tries in the dying minutes.
England Under-18s coach John Fletcher said: This is the first rugby these lads have had in 12 weeks and they put on a good performance. Tucuman have a great passion for rugby and they showed that in this game, but also in their hospitality with over 2,000 people coming to watch the match.
England face Buenos Aires Under-18s on Wednesday before taking on Mendoza Under-18s and the Argentina Under-18 side.
1 Joe Marler (Harlequins, captain), 2 Jamie George (Saracens, Haileybury), 3 Mako Vunipola (Bristol Rugby, Millfield), 4 Tom Holmes (Sale Sharks, Sandbach), 5 James Gaskell (Sale Sharks, Sandbach), 6 Will Welch (Newcastle Falcons, RGS Newcastle), 7 Joe Barker (Leeds Carnegie, QEGS Wakefield), 8 Jamie Gibson (London Irish, Marlborough College), 9 Sam Harrison (Leicester Tigers, John Cleveland College), 10 Freddie Burns (Gloucester Rugby, Bath College), 11 Will Hurrell (Leicester Tigers, Queen Elizabeth II), 12 Owen Farrell (Saracens, St Georges), 13 Andy Forsyth (Leicester Tigers, QEGS Wakefield), 14 Marcus Watson (London Irish, St Georges College), 15 Jack Wallace (London Wasps, RGS High Wycombe).
Replacements: 16 Peter Austin (London Irish, Worthing College), 17 David Blackwell (Gloucester Rugby, Hartpury), 18 Joe Quinn (St Wilfred's School, Leeds Carnegie), 19 Sam Jones (London Wasps, Aylesbury Grammar), 20 Jordi Pasqualin (Gloucester Rugby, The Kings School), 21 Rory Clegg (Newcastle Falcons, Barnard Castle), 22 Sam Edgerley (London Irish, Wellington College), 23 Joe Cobden (Leicester Tigers, King Edward VI Lichfield).
Substitutions: Austin for Vunipola, Blackwell for George, Edgerley for Hurrell, Quinn for Gaskell (all 52mins), Pasqualin for Forsyth (57), Jones for Gibson (63), Clegg for Wallace (66)