Full-time from The Den
The young Lions, including three over-age players in the shape of defender Mark Beevers, winger Gueye and midfielder Angel, were good value for the victory despite the narrow scoreline, and indeed could have won by a bigger margin had Alfie Pavey's 77th-minute penalty not been saved.
Millwall got off to a perfect start when Gueye broke the deadlock after just six minutes. Left-back Dylan Casey picked out the winger with a neat pass, and he in turn took a touch before firing home the opener from the edge of the box.
It could have been 2-0 just moments later when an intelligent through ball from Jack Powell found Pavey in space. Unfortunately the young striker fired over the bar from a good position.
Powell's range of probing passes so nearly paid off midway through the opening half, but striker Jamie Philpot was a whisker away from connecting with his team-mate's 40-yard delivery.
The Lions continued to search for a second goal before half-time and it so nearly arrived on 31 minutes when Philpot won possession high up the pitch and sent over a cross that was met by Pavey. On this occasion Crewe keeper Liam Matthews was equal to Pavey's powerful header and made a smart stop on the line.
Crewe's Callum Saunders looked odds-on to score soon after the restart when he latched onto an under-hit back pass from Ben Thompson, however Beevers came to the rescue with a perfectly timed intervention to clear the danger.
The visitors played with greater cohesion during the second-half and were denied an equaliser by the brilliance of keeper Jordan Archer, who somehow kept out Liam O'Neill's goalbound shot with his legs to protect The Lions' 1-0 ahead.
That seemed to spark the home side into life, and they responded in a positive fashion with Gueye close to adding a second goal on 74 minutes, but his low drive was blocked by midfielder Josh Green.
However The Lions now had the bit firmly between their teeth and when Powell's delightful free-kick was handled in the penalty area after 77 minutes, Millwall had a perfect opportunity to put the game to bed.
Up stepped frontman Pavey to take the resulting spot-kick, only for Crewe keeper Matthews to guess right, diving low to his left to save the penalty.
Pavey, Powell and Angel were involved in a neat move four minutes later that finished with a cross-shot from Philpot dipping narrowly over the bar, and The Lions were pegged back on level terms soon after.
There were just seven minutes remaining when a corner was swung deep into the Millwall penalty area and Crewe substitute Chris Speed eventually smuggled the ball over the line following a goalmouth scramble.
The Lions were not done for, however, and with the game entering the 89th-minute midfielder Angel made no mistake to fire home the match-winner from close range after his initial shot had been blocked.
Millwall: Archer, Siafa, Wood, Beevers, Casey, Powell, Thompson, Angel, Gueye, Pavey, Philpot. Subs not used: Sandford, Brown, Eze, Mundle-Smith, Parr.