Ibrahimovic, PSG keep pace with Lyon
Ezequiel Lavezzi added a fourth with eight minutes to go for PSG, which also hit the post.
Ibrahimovic has now taken his tally to 17 in the league since arriving from AC Milan in the offseason. The Sweden striker has equaled his third best record in an entire campaign with more than half the season remaining.
Dario Cvitanich scored the only goal of the game from the penalty spot after both Jean-Armel Kana-Biyik and Yassine Jebbour had been sent off.
Ibrahimovic scored his first in the 28th minute. Jeremy Menez's cross was punched clear by Valenciennes goalkeeper Nicolas Penneteau, but only as far as Lavezzi, whose shot was deflected in by Ibrahimovic.
PSG was hit by a setback just before halftime when Alex was forced off with an injury to his right thigh. He was replaced by Mamadou Sakho.
Ibrahimovic doubled his tally four minutes after the break. Valenciennes defender Rudy Mater's clearance fell to Javier Pastore who unleashed a powerful volley which Penneteau could only push straight out to the feet of Ibrahimovic who was completely alone, six yards (meters) out.
The Swede completed his hat-trick five minutes later. Lavezzi sent a great through ball in to Menez who slotted it across the area for Ibrahimovic to drive home.
Ibrahimovic scored 17 league goals in a season for Inter Milan in 2007/08 but has only bettered that tally twice, in the following year at Inter - when he scored 25 - and his final season at Milan - when he scored 28.
Blaise Matuidi also hit the left post for PSG before Lavezzi extended its lead late, firing home Marco Verratti's pass.
Meanwhile, in Nice, matters started to go wrong for Rennes in the 53rd minute when Kana-Biyik was shown a second yellow card and sent off following a poor tackle on Cvitanich.
Jebbour was also harshly sent off 10 minutes later for what was adjudged to have been a push on Nice striker Eric Bautheac in the area.
Cvitanich fired the resulting penalty to the left of Rennes goalkeeper Benoit Costil for his 10th goal in his last 12 games.