Crow's strike was his first goal since joining Luton
Second-half goals from Danny Crow and Amari Morgan-Smith spared Luton's blushes as they missed three penalties on the way to beating 10-man Mansfield.
Claude Gnakpa and Crow both had a retaken spot-kick saved by Alan Marriott, while Matthew Barnes-Homer blasted the third over the bar.
The Stags also had Stephen Foster sent off for two bookable offences before Crow fired Luton ahead from 12 yards.
Morgan-Smith then marked his Hatters debut by netting with a fierce drive.
The 21-year-old only joined the Hatters on Tuesday after his former club Ilkeston Town were wound up earlier this month.
He saw Gnakpa force a fine save out of Marriott before the penalty drama began just before the break when Foster handled the ball and was booked for dissent.
Gnakpa's penalty was saved by Marriott, but referee Steve Cook ordered a retake and the keeper was again equal to Crow's effort, pushing it around the post.
There was still time for Foster to collect his second booking before the interval, and Luton were awarded a third penalty seconds after the restart when Chris Smith fouled Gnakpa.
This time Barnes-Homer stepped up but missed the target. Luton did not have to wait long to make the breakthrough, though, as Crow fired home before Morgan-Smith sealed the points.
Luton:
Tyler, Gleeson, Kroca, George Pilkington, Fred Murray, Gnakpa, Keane, Howells, Morgan-Smith (Newton 81), Barnes-Homer (Adam Murray 71), Crow (Atieno 84). Subs Not Used: Kevin Pilkington, Blackett.
Booked: Keane, Barnes-Homer.
Goals: Crow 51, Morgan-Smith 54.
Mansfield: Marriott, Silk, Foster, Chris Smith, Sandwith, Istead (Briscoe 68), Nix, Mills, Adam Smith (Naylor 46), Connor, Duffy (Medley 52). Subs Not Used: Collett, Stonehouse.
Sent Off: Foster (45).
Booked: Sandwith, Istead, Foster, Chris Smith, Medley, Mills, Silk.
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