Di Maria grabbed the opener late in the first half and Lucas doubled PSG's lead just after the hour mark.
Angel Di Maria's first goal of the season set Paris Saint-Germain on their way to a 3-0 Champions League victory against an unlucky Basel side at the Parc des Princes on Wednesday.
Di Maria grabbed the opener late in the first half and Lucas doubled PSG's lead just after the hour mark before Edinson Cavani's late penalty sealed the victory as the French giants moved closer to qualifying for the last 16 from Group A.
They remain level on seven points at the top of the group with Arsenal, who crushed Ludogorets 6-0 in London, with Basel and the Bulgarians both six points behind.
A draw when they play Basel away in their next outing will likely secure their progress to the next round, and yet the outcome of this game could have been very different, with the Swiss side hitting the woodwork three times.
"Fortunately we had luck and Alphonse (Areola) on our side, and good posts as well," midfielder Adrien Rabiot told Canal Plus after the game.
"You need luck in these matches. But we controlled the game too and the main thing is that we won."
The home side were without the injured Thiago Motta, and while the elegant Rabiot started in his place, they missed his ability to dictate the tempo of a game and keep possession.
Indeed, a side that had appeared so accomplished in previous seasons under Laurent Blanc again looked a shadow of their former selves for much of this game.
Paris have not yet convinced under Unai Emery and they could not afford to underestimate a Basel outfit utterly dominant in their domestic league and who have pulled off some impressive results in Europe.
The visitors were the better team in the first half but missed several chances, first when Birkir Bjarnason kept alive a corner at the back post and Michael Lang headed against the bar.
Ivory Coast striker Seydou Doumbia then outmuscled Thiago Silva before releasing Renato Steffen, but Alphonse Areola came out to deny the winger before Doumbia fired over the loose ball.
Di Maria did flash a volley just past after being teed up by Lucas on a quick breakaway but Basel hit the woodwork again in the 36th minute, this time from a Doumbia header after a Matias Delgado cross.
Rabiot was denied by Tomas Vaclik seconds later but Paris were poor, and yet they went in front five minutes before the interval.
Cavani tried to convert a low ball in by Blaise Matuidi but his touch turned into an assist for Di Maria, who finished emphatically.
Cavani saw a header graze the near post on its way past as he connected with a Di Maria free-kick at the start of the second half.
He then robbed Eder Balanta and bore down on goal but could not beat Vaclik. Instead, it was Lucas who made it 2-0 moments later, slotting low into the net after Basel failed to cut out a Serge Aurier centre.
It was not Basel's evening, and they hit the frame of the goal for the third time in the 66th minute. Marek Suchy's header following a free-kick struck an upright and then rebounded off an unwitting Areola on the line.
Cavani then added gloss to the scoreline by converting a stoppage-time penalty for his 17th goal this season for club and country after he had been fouled in the box.