Phil Parkinson’s men played with confidence from the outset as Kieffer Moore and Issa Kabore both tested Max Crocombe early on.
But the Lions settled and could have gone ahead on 27 minutes as Camiel Neghli nipped in front of Kabore at the back post, although he could only head Tristan Crama’s cross over.
Following a prolonged quiet spell, Azeez blazed over in the final seconds of the opening half to ensure the contest remained finely poised.
Having already lost Matty James – who has featured in every league game so far this season – to injury in the first half, Wrexham’s left wing-back Liberato Cacace was forced off shortly after the restart.
Those blows did not dampen the spirits of the home side as Moore twice got into promising positions either side of Callum Doyle’s driven effort at goal.
But Millwall took the lead in fortuitous circumstances as Azeez’s cross was turned into his own net by Cleworth from close range.
Substitutes George Thomason and George Dobson both had efforts as the Red Dragons – who rank third in the Championship for most points won from losing positions – pushed for an equaliser.
Defender Dom Hyam then headed over from a set-piece as Parkinson sent on Josh Windass, new signing Davis Keillor-Dunn and Smith.
Smith, who had scored in each of his past four league starts, spurned two huge opportunities in the space of a minute after Coburn was unable convert from close range at the other end.
But the Millwall substitute made no mistake in the 85th minute as he rifled beyond Arthur Okonkwo to seal victory with his side’s first effort on target.