Eriksen scored from 30 yards at Camping World Stadium to draw Spurs level after Edinson Cavani's opener in the International Champions Cup clash.
PSG goalkeeper Kevin Trapp endured a miserable outing, his error gifting Eric Dier a goal to put Tottenham ahead.
A thrilling first half saw four goals scored, with Javier Pastore equalising for PSG.
The second half was quieter, with Spurs winning thanks to Alderweireld and a Harry Kane penalty after playing against 10 men following Trapp's sending off.
While this marked PSG's second game at the ICC, it was Spurs' first match in almost two months, but both teams played with plenty of energy.
PSG started brightly and Cavani headed wide after just 30 seconds, but his second chance would be the opening goal.
The Ligue 1 giants broke well down the left, Adrien Rabiot bursting in behind before crossing for Cavani to apply a side-footed finish.
However, Spurs were level just five minutes later and in spectacular fashion.
After receiving a pass from Georges-Kevin N'Koudou, Eriksen's 30-yard effort gave Trapp no chance as it found its way in via the underside of the crossbar.
There were plenty of chances at both ends and another goal followed in the 18th minute.
Under heavy pressure, Trapp tried to play a pass out, but Dier intercepted and saw his block go into the back of the net.
After a drinks break, PSG levelled through Pastore nine minutes before half-time.
Left in plenty of space down the left, Pastore took a pass from Rabiot before skipping into the box and finishing into the top corner.
Dier struck the woodwork with a header late in an entertaining half, and Trapp's nightmare continued seconds into the second.
A long pass over the top appeared set to cause the goalkeeper no danger, but he inexplicably handled outside his area and was sent off.
Substitute goalkeeper Alphonse Areola made a save from Kane's free-kick as Spurs always looked like capitalising on their numerical advantage.
Eriksen almost struck from distance again in the 71st minute before Tottenham finally went ahead once more through Alderweireld.
The defender received a pass from Victor Wanyama before unleashing a 25-yard strike into the bottom corner.
Kane sealed the win with a powerful penalty in the 88th minute after a handball in the area.