Mark Rivers forced a decent early save out of Kelvin Davis before Ipswich went ahead on six minutes - Ian Westlake winning a loose ball and playing in Kuqi who coolly stroked the ball beyond Clayton Ince.
On 12 minutes, it was 2-0 with Westlake again the provider, playing the ball forward to skipper Magilton, who turned Billy Jones before firing a low 20-yarder through the defender's legs and wide of Ince.
A dangerous Darren Bent cross was scrambled away as Town continued to press, but in a rare Crewe attack, Vaughan left Fabian Wilnis on the ground, but his ball in was grabbed by Davis as Rivers closed in.
Bent curled a shot narrowly wide, then forced Ince to save an angled shot with his legs before Kuqi rose to meet a Magilton corner but looped his effort over.
Luke Varney nearly touched home a Lee Bell low ball after he skipped beyond David Unsworth, and in the final action of the half, Bent's shot on the turn was well fielded by Ince.
Bent got in behind the Crewe defence on to a clever Darren Currie reverse ball, bundled his way beyond Ince, but couldn't keep the ball in play as Ipswich started the second half on top.
As in the first half, Ipswich broke through six minutes into the period, Miller criminally being allowed to stride up to the edge of the Crewe box, from where he calmly curled his shot around Ince.
A Westlake 30-yarder was deflected, making an easy save for Ince, before Rivers - who had a trial spell with Ipswich last summer - drilled a firm shot just over from Varney's pass.
Varney should have found Rivers after leaving sub Drissa Diallo on the deck, before Ince had to be alert to stretch and catch a deflected Magilton effort.
Magilton fired another shot wide before Town scored their fourth on 81 minutes when sub Counago's throughball was cut out, but picked up by Miller 20 yards out, who beat Ince with a firm low shot, although the keeper got a hand to it.
A minute later it was 5-0 as Bent steamed down the right flank and produced a perfect cross for Counago to smash a volley into the roof of the net from seven yards.
A rare mistake by Davis allowed Vaughan to pull a goal back in the final minute when the keeper spilled a tame 25-yarder and then palmed it in off the post.
Ipswich will now go up in second if they get a better result at Brighton than Wigan do at home to Reading, while Crewe must beat Coventry at home and hope other results favour them to survive.