Player-boss Wise's late surge into the penalty box was ended when he was tripped allowing Ben May - a late replacement for Danny Dichio - to slam home an emphatic spot-kick on 85th minute to give Millwall a crucial three points.
The Lions seemed to be coasting to a comfortable victory after goals from Barry Hayles, Marvin Elliott and Jody Morris put them 3-0 up after 50 minutes, but relegation threatened Crewe staged a remarkable comeback inspired by livewire striker Steve Jones.
His thumping strike sandwiched a Kenny Lunt penalty on 61 minutes and Luke Varney's late leveller on 81 minutes.
But the gutsy Gresty Road side's hopes of gaining a vital point were dashed when May's decisive penalty sent the New Den into ruptures.
However, the thrills and spills of a thrilling second half were in stark contrast to a scrappy first 45 minutes.
Crewe, hoping to edge clear of a relegation battle, wove pretty pictures in the midfield but lacked a killer punch.
Millwall striker May carved out the first real chances of an eventful encounter and the Lions' growing ascendancy was rewarded with Hayles' goal on 26 minutes.
The frontman scored his tenth league goal of the season when he cut in from the right and curled a 15-yard shot past Ben Williams in the Crewe goal.
Midfielder Peter Sweeney nearly doubled the Lions' advantage when his savage shot was tipped over the bar by Williams.
Luke Varney almost drew Crewe level in first-half injury-time when his shot struck a post with Andy Marshall in the Millwall goal well beaten.