The goal came in the 16th minute, when the experienced striker notched his 111th goal for the club and put them in front as Walsall's wobbly defence got into trouble.
A long ball down the middle from defender Paul Robinson was seized on by Harris, who turned past Rhys Weston to fire a low shot across keeper Clayton Ince and into the far corner.
Harris continued to be a thorn in the Saddlers' side, but to their credit the home side fought back and equalised in the 28th minute.
Chris Palmer's corner was partially cleared, but the Walsall full-back took possession again and sent over a dangerous cross which was headed back by Michael Ricketts for Alex Nicholls to score his fourth goal in as many games.
Milwall, however, were the better side throughout the first half, but both Chris Hackett and Tresor Kandol missed great chances.
Ricketts had a volley blocked 11 minutes before the interval, but Milwall settled again and began to dominate the second half.
In the 88th minute, Kandol was presented with a great chance by a cross from Karl Moore, but failed to test Ince, who saved comfortably.
Milwall looked the more cultured side and their overall superiority was rewarded in the 89th minute following a corner by Moore.
The ball bobbled around the Walsall area before Lions left-back Andy Frampton scored with a low header to maintain his side's push for promotion.
Walsall kept fighting, despite chants from the crowd for the head of manager Jimmy Mullen and in added time Anthony Gerrard and Troy Deeney had efforts which failed to find the target.