Tuttle, having guided the Lions to two draws, made a triple substitution at half-time with his team trailing 1-0 to fellow strugglers Brighton.
The changes paid off immediately with goals in the space of four minutes at the start of the second half by Ben May and substitute Josh Simpson.
The surprise turnaround followed a disastrous start for Millwall as they fell behind in only the third minute.
A free-kick from close to the corner flag by Brighton's French winger Alexandre Frutos was headed in at the far post by Dean Hammond, his fourth of the season and first for two months.
Brighton went on to control the first half and had chances to extend their lead.
The best of them fell to Hammond in the 42nd minute when the home side broke quickly following a mix-up in the Millwall ranks. It left Brighton with a man over and Mark McCammon put Hammond clean through but Colin Doyle made a vital save.
Millwall thought they had levelled a minute later when Kevin Braniff headed in a Jody Moris free-kick but it was ruled out for Bruce Dyer pulling a Brighton player inside the area.
Dyer, Braniff and on loan Liverpool defender Zak Whitbread were all substituted by Tuttle at the break.
The changes were instantly rewarded in the 47th minute when Barry Cogan, one of the replacements, released Alan Dunne for a cross-cum-shot which May volleyed in.
The match was turned on its head three minutes later as Simpson, another of the substitutes put the visitors ahead.
A shot by Morris was blocked after a one-two with Cogan and Simpson pounced to turn in the loose ball from 10 yards as the Brighton defence dallied.