Neuville carried his strong form into the final day to dominate the morning loop, winning the opening SS13 stage.
That stage win meant he closed the gap to leader Evans down to 1.4s, and overhauled Sebastien Ogier for second place in the process.
In the following La Cabanette - Col De Braus test, the Hyundai driver went 5.4s faster than the Evans to take the lead with a four-second gap to the 2017 WRC Wales Rally GB winner.
Ogier had a tough morning, losing 6.2s to Neuville in the La Bollene Vesubie - Peira Cava run and a further 6.5s to the Hyundai in the next stage, meaning he is now in third, 6.1 seconds off the lead.
The seven-time WRC Monte Carlo Rally winner admitted that the 13.36km La Cabanette- Col De Braus test wasn’t a “great stage" for him and that he wasn’t “perfectly comfortable”.
Hyundai driver Sebastien Loeb was lucky to remain in the rally after locking up at a hairpin in the middle of SS14.
The nine-time WRC champion went off the road, leaving his Hyundai teetering on the edge of a drop, but he was pushed back on to the road by spectators and was able to continue to the end of the stage.
That incident cost Loeb over 20 seconds and he has dropped behind Esapekka Lappi to fifth, which leaves him 16.7s behind the M-Sport driver going into the final two stages of the rally.
Kalle Rovanpera is in a lonely sixth place in his Toyota Yaris, and he took the opportunity to test different tyre combinations.
Another Toyota driver Takamoto Katsuta is in seventh place and a further seven minutes behind the 2019 WRC2 champion, while Eric Camilli is still leading the WRC3 class in his Citroen C3 and is eighth overall.
M-Sport driver Teemu Suninen had a strong morning and has moved up to the top 10, ending the morning loop in ninth place.
Mads Ostberg is the leading WRC2 driver and rounds out the top 10 in his Citroen C3, 29.9s ahead of WRC3 competitor Nicolas Ciamin, who has dropped down to 11th.