Vladimir Weiss cancelled out Edinson Cavani's opener with a fine individual effort in the first half, before Motta headed home from two Ezequiel Lavezzi corners to put the visitors in control.
Young debutant Marquinhos added a fourth in the remaining few minutes, in what was eventually a convincing win for Laurent Blanc's side in their UEFA Champions League opener.
Olympiacos made three changes from the side that beat Xanthi at the weekend, with Javier Saviola, Kostas Manolas and Leandro Salino making way for Giannis Maniatis, Alejandro Dominguez and Dimitrios Siovas.
The Ligue 1 outfit handed a debut to 19-year-old Marquinhos, who was drafted in for the injured Alex.
Javier Pastore was ruled out with a foot injury, while Cavani was welcomed back to the starting line-up having been named on the bench for the weekend win over Bordeaux.
Like PSG, Olympiacos recruited a number of players during the transfer window, including former Rangers playmaker Weiss, who very nearly gave his team the perfect start after he sent a stinging long-range effort crashing off the bar within the first minute.
It was a sign of things to come from the Slovakian, who was given another chance 10 minutes later, rifling a low shot just past Salvatore Sirigu's near post.
The Turkish goalkeeper's woodwork was struck again a few minutes later thanks to David Fuster's looping volley as the home side continued to search for an opener.
They were made to pay for their wastefulness three minutes later, however, when Zlatan Ibrahimovic threaded a perfectly weighted ball into the path of Maxwell, who squared for Cavani to tap into an empty net.
But the goal failed to discourage Michel's side and they were duly rewarded for their persistence just six minutes later thanks to a fine individual effort from Weiss.
The winger picked up the ball on the right before cutting inside to shake off first Marquinhos and then Thiago Silva, before sending a flicked shot into the bottom corner of the net.
It was no less than they deserved as PSG struggled to maintain possession for large periods of the first half.
The visitors looked more settled after the break, but struggled to carve out an opportunity until the hour mark when Cavani forced a smart save from Roberto.
PSG gradually began to press, and took the lead for the second time after 68 minutes when Motta beat his marker to power home a header from Lavezzi's corner.
Olympiacos did not appear to learn their lesson and that move was recreated three minutes later, with Motta beating the challenge of Andreas Samaris to once again head home.
Michel threw on Javier Saviola in an attempt to regain a grip on the game, but the experienced striker could not stop his conceding again five minutes from time.
The home side once again failed to deal with a teasing cross into the box, leaving Marquinhos to direct a header past Roberto.
