The home side have now gone 16 Championship games without a victory and appear destined for League One football next season, but they took the lead in the 15th minute when livewire Luke Rodgers turned and fired across the six-yard box and Steve Jones helped the ball in from close range.
Rodgers had already lifted the home crowd with a surging run which carried him from deep inside his own half to the Ipswich box, but his finishing let him down and he pulled his effort wide for the far post.
But nevertheless Crewe had started brightly, but their failings this season have been mainly in defence and for the third game running they failed to preserve a lead, conceding within three minutes after some dreadful defensive work gifted Lee a headed finish.
When Matt Richards lofted the ball into the home box there seemed little danger, but Steve Foster and Kenny Lunt were caught ball-watching as Lee emerged from nowhere to finish past keeper Ross Turnbull.
Lee limped off with an injury just after the half-hour mark, but that didn't knock Ipswich out of their stride.
Substitute McDonald came close with a cross across the face of the goal and Turnbull needed to palm Jimmy Juan's free-kick over the bar as the East Anglians got on top of the game.
Steve Jones came close to a second with a stunning 20-yard volley which dropped over just after the break, but it was a rare moment of Crewe excitement.
With veteran Jim Magilton introduced on the right, Ipswich called all of the shots and McDonald looked very lively.
Never more so than when he edged Town in front in the 52nd minute, taking Richards' diagonal pass before nutmegging John Otsemobor to finish with a low shot off the far post.
Steve Foster missed two decent chances when he headed a Lunt free-kick straight at Shane Supple and lifted a corner from the same player over the bar.
But Crewe lacked ideas as well as possession as Ipswich finished in the comfort zone.