Things turned sour for the Lions after 43 minutes when Jed Wallace was dismissed for a challenge on Kieran Lee, referee Gavin Ward consulting his assistant Ian Cooper before brandishing the red card.
Despite Wednesday laying siege to the home goal, the Londoners hung on for three points that moves them on to seven for the season.
Both teams will have been buoyed going into this encounter after strong starts to the season.
However, there was little to write home about during the opening exchanges, with neither team possessing the urgency and precision to unlock the opposition.
Millwall's brightest spark early on was Mahoney and his searching deliveries were a constant source of worry for the Wednesday defenders.
For the visitors, it was Kadeem Harris and Adam Reach who looked the most likely source of inspiration.
Harris' acquisition from Cardiff has proved shrewd, with the diminutive winger seeing his cross sail across the face of Bartosz Bialkowski's goal.
Long-distance specialist Reach then almost had another gem to add to his collection, but the 26-year-old's speculative right-footed effort flew just over Bialkowski's crossbar.
It was a Mahoney set-piece that led to the breakthrough after 37 minutes. The 22-year-old, signed from Bournemouth in the summer, sent in a pinpoint cross, which Smith emphatically met at the back post.
However, the mood darkened considerably when a melee ensued following a Wallace challenge on Lee.
After a short discussion between the two officials, the former Wolves winger was given his marching orders, which raised the decibel levels a few notches.
Lee Bullen's men looked to make full use of their man advantage immediately after the break, but Steven Fletcher's effort was gobbled up by Bialkowski.
Mahoney's presence, though, continued to prove a problem for the South Yorkshire outfit and another teasing ball in was glanced over the bar by Smith.
It was then Aiden O'Brien's turn to almost make it 2-0 after 57 minutes, but his thumping drive from inside the box was pushed over the top brilliantly by Keiren Westwood.
The pace of the game quickened considerably after the interval, but it was then Wednesday's turn to go close on a couple of occasions, with their best chance coming when Bialkowski palmed away a curling shot from recent introduction Barry Bannan.
The on-loan Ipswich keeper then repelled a Sam Hutchinson half-volley before Harris flashed another tantalising ball across goal.
However, the Millwall rearguard held firm for a well-earned three points.