Full-time from Gresty Road
O'Brien, making his first League One start of the season, opened The Lions' account on 21 minutes with a poacher's goal and although Crewe levelled with a fortuitous header from Lauri Dalla Valle (36mins), O'Brien added two crackers on 64 and then 74 minutes to complete his treble.
It was a thoroughly deserved victory for Neil Harris' charges, who played with energy, skill and increasing confidence as the game wore on.
Millwall showed two changes from the side that beat Peterborough United last time out with Jimmy Abdou and Steve Morison returning to the starting XI at the expense of Ben Thompson and John Marquis, both of whom dropped to the bench.
Nelson was involved at the other end three minutes later with a superbly timed interception to clear the danger as Bradden Inman broke through into the penalty area.
Back came The Lions though, and Steve Morison bamboozled the Crewe rearguard with some neat footwork on 12 minutes before forcing keeper Ben Garratt into a smart save to keep out his snap-shot.
However there was little Garratt could do to prevent The Lions from breaking the deadlock after 21 minutes. Right-back Carlos Edwards was involved again with a fine run on the overlap, delivering an inviting cross that Morison met with a stinging drive which was blocked by the keeper. The ball fell to O'Brien, who turned on a sixpence with his back to goal and arrowed a drive that flew into the back of the net.
Millwall really had the bit between their teeth now and pushed forward in search of a second goal. The pace of Fred Onyedinma and O'Brien seemed to frighten the life out of the Crewe defence as the young Lions teased and tormented a hesitant looking rearguard. After another neat move, O’Brien couldn’t quite on the end of Onyedinma's cut back but after the ball was cleared, Ed Upson's volley landed on the top of the net.
Morison was a whisker away from connecting with the influential Williams' diagonal ball as The Lions kept their foot on the gas, but it was Crewe who stunned their opponents scoring an equaliser against the run of play nine minutes before the interval. The ball ricocheted in the penalty area following Inman's shot and Dalla Valle got the final touch past the wrong-footed Jordan Archer, although the Crewe man seemed to know little about it as the ball slammed off his head.
Millwall weren't put off by the misfortune however, and the tireless Morison's sublime skill almost restored their lead, controlling a high ball expertly, giving Harry Davis the slip, only to send his effort from the edge of the box straight into Garratt's hands.
Webster nearly scored within 60 seconds of arriving on the field, but just couldn't direct his header from a Williams' corner towards goal, and the ball flew over the bar.
However, The Lions were indebted to keeper Archer soon after when Crewe's Davis found himself clear after a front post corner was missed, Archer saved his shot and then brilliantly turned Dalla Valle's follow-up round the post.
The volume was cranked up a further notch when O'Brien completed his hat-trick with another sublime goal. Picking up the ball 20 yards out, he ghosted his way past four defenders with some superb close control and cracked home a powerful effort past the outstretched hand of Garratt. Cue a mass celebration as the young striker disappeared under a mass of his jubilant team-mates!
Booking: Davis (60mins)
Scorer: Dalla Valle (36mins)
Millwall: Archer, Edwards, Craig, Nelson (Webster, 51mins), Beevers, Abdou, Williams, Upson, Onyedinma (Ferguson, 69mins), Morison, O'Brien (Gregory, 84mins). Subs not used: Forde, Thompson, Marquis, Cowan-Hall.
Booking: Webster (90+1min)
Scorer: O'Brien (21, 64, 74mins)
Ref: D. Handley