Eriksen's piledriver to level the scores on 11 minutes was worthy of any stage and Alderweireld's arrowed drive to hand us a 3-2 lead eight minutes from time was another strike right out of the top-drawer.
Eric Dier and Harry Kane were also on the scoresheet as we impressed at the Camping World Stadium in Orlando, Florida.
It was an eventful night - six goals and a straight red card for PSG's German international goalkeeper Kevin Trapp for deliberate handball outside his penalty area.
Also worth mentioning - Harry Winks made a welcome return to action as a second half substitute, his first outing since his serious ankle injury at Burnley on April 1. Meanwhile, Academy graduate Tashan Oakley-Boothe made his debut at this level and played for the full second half.
Below: Victor Wanyama battles with Jese
The players felt they started sloppily and after a couple of early chances, were punished on six minutes as PSG broke down the left and Adrien Rabiot squared for Edinson Cavani to slot home the opener.
It didn't take long for us to respond though - and what a response! Picking up the ball in space centrally, Eriksen needed no second invitation and his thunderbolt from 30 yards ripped home off the underside of the crossbar.
We took the lead on 18 minutes through sheer determination from Dier. Rabiot played the ball back, Dier was on the charge closing down and continued his run to block Trapp's attempted clearance and watch gleefully as the ball rebounded back into the empty net.
Both teams had further chances in an entertaining first half with Ben Davies and Georges-Kevin Nkoudou close for us but PSG levelled before the break when Javier Pastore found himself in space left side, shifted right and pinged into the top corner.
The game took another turn barely 20 seconds into the second half. We made eight changes at the break and Kane, one of those eight, looked favourite to get to a ball over the top, only for Trapp to charge out of his penalty area and handle the ball. Kane would have had an empty goal in front of him and the referee was left with little option but to show the red card.
His replacement Alphonse Areola made an instant save from Eriksen and further denied Dele Alli and Victor Wanyama. You always felt a goal was there and it arrived eight minutes from time through Alderweireld, who drilled low across Areola into the far corner from 25 yards.
Kane provided the icing on the cake when Blaise Matuidi was penalised for handling Kieran Trippier's cross in the penalty area and the England striker made no mistake, using power this time to blast home from the spot for 4-2.
MAURICIO POCHETTINO SAID
"Winning is always a good habit. It’s true that today it’s not the most important thing because our priority is not the result but if you win it’s always better. We need to keep that mentality and keep the same feeling from how we finished last season."
Paris Saint-Germain (first half): Trapp, Alves, Kimpembe, Marquinhos, Kurzawa, Motta, Rabiot, Guedes, Pastore, Giovani Lo Celso, Cavani.
Paris Saint-Germain (second half): Trapp, Alves (Nkunku 68), Kurzawa (Yuri 68), Marquinhos, Kimpembe, Matuidi, Guedes (Areola, 46), Pastore (Di Maria 68), Motta (Callegari 68), Bernede, Jese.
Spurs (first half): Lloris (c), Walker-Peters, Carter-Vickers, Vertonghen, Davies, Dembele, Dier, Eriksen, Onomah, Nkoudou, Janssen.
Spurs (second half): Vorm, Trippier, Alderweireld, Wimmer, Davies, Dembele (Winks 60), Wanyama, Oakley-Boothe, Eriksen, Dele, Kane.
Goals: PSG - Cavani 6, Pastore 37; Spurs - Eriksen 11, Dier 18, Alderweireld 82, Kane 88 (penalty).
Yellow cards: PSG - Jese 59; Spurs - Alderweireld 70.
Red card: PSG - Trapp 46.
Our second of three ICC matches in the USA is against Italians AS Roma at the Red Bull Arena in Harrison, New Jersey on Tuesday evening (8pm KO local time, 1am UK). We then take on Manchester City in Nashville on Saturday (5pm local, 11pm UK).