Second-half goals from Alan Dunne and Will Hoskins got new Millwall boss Kenny Jackett off to a flying start. The Robins snatched the lead on half time when Chris Senior volleyed home.
Millwall were handed a lifeline when Chris Lane handled Gary Alexander's shot and was sent off, with Dunne firing the penalty past Stuart Coburn.
And on-loan Watford striker Hoskins secured the Lions' passage into the next round when he fired Jay Simpson's pass past the exposed Coburn.
Altrincham: Coburn, Lane, Tinson, Shotton, Scott, Lawton, Sedgemore, Peyton (Munroe 80), O'Neill (Logan 64), Little, Senior (McFadden 85).
Subs Not Used: Acton, Aspinall.
Sent Off: Lane (53).
Goals: Senior 45.
Millwall: Pidgeley, Dunne, Whitbread, Robinson, Bignot, Simpson, Brkovic, Hodge, Bakayogo, Alexander, Hoskins.
Subs Not Used: Day, Barron, Fuseini, Gaynor, O'Connor.
Booked: Bakayogo.
Goals: Dunne 53 pen, Hoskins 62.
Att: 2,457
Ref: Eddie Ilderton (Tyne & Wear).
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Interview: Altrincham manager Graham Heathcote
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