Neuville started the loop with a 29.9s advantage over Evans, but the Welshman reduced the gap to 23.6s in the opening stage of the afternoon at Viera do Minho.
But the Hyundai driver extended his lead to 28s on the Cabeceiras de Basto stage and then stretched his lead by a further 11.8s on the long third stage at Amarante.
It rained on sections of both the second and third stages which suited Hyundai's decision to run with four soft tyres compared with Ford's two.
Evans takes world championship lead with Sweden win
16/02/2020 AT 16:10
It means Neuville is on target to take advantage of Sebastien Ogier's retirement from the rally after a crash on Friday.
Evans was able to move clear of Neuville's team-mate Dani Sordo in third place overall and ended the day 17.4s clear of him, having been just 5s ahead at the start of the afternoon loop.
Sordo came under pressure from M-Sport's Teemu Suninen in fourth and the Hyundai man had a half-spin at the start of the final stage which lost him around 7s, but recovered to end the day 4.7s clear of the Finn.
Suninen finished 11.1s ahead of Toyota's Esapekka Lappi in fifth after a close fought battle throughout the day, with Suninen also benefitting from a review of previous times which gained him 6.4s.
He had previously earned notional times after getting stuck behind Hayden Paddon following his crash that blocked the route and ended up with the New Zealander being airlifted to hospital.
Citroen's Mads Ostberg and Craig Breen are a distant sixth and seventh overall after delays earlier in the rally.
Ostberg also lost over a minute to the leaders on the second stage of the afternoon due to a half-spin which left his rear wheels over a dip and requiring spectators to push him back on course.
Citroen's Kris Meeke had been airlifted to hospital following his earlier crash, but has now been released after precautionary checks
Tanak wins in Chile, Ogier retakes championship lead
12/05/2019 AT 20:06
World championship leader Neuville crashes out in Chile
11/05/2019 AT 17:38