Lowe, on loan from Wolves, struck in the 75th and 90th minutes to lift Vale off the bottom of the table and give Sinnott a much needed tonic.
Vale debutant Chris Herd, on loan from Aston Villa, was lively in the opening exchanges before Millwall took the lead with their first effort on goal in the 14th minute.
Ex-Vale midfielder Dave Brammer bent in an inviting cross from the right and Gary Alexander met it with a bullet header which scraped against Joe Anyon's left-hand post on its way in.
The goal momentarily stunned Vale but they were soon fighting back as Lowe's header drew a flying save from Lenny Pidgeley.
An equaliser was due by the time it arrived in the 24th minute, although Vale did need some poor defending by the visitors before Danny Whitaker slotted his second goal in as many games.
A long cross from Paul Harsley led to Danny Senda knocking the ball past Pidgeley and Whitaker gleefully slammed his shot into the roof of the net.
Vale remained in the driving seat as half-time approached and Pidgeley had to move smartly to tip a 25-yard drive from the impressive Whitaker over the bar.
The game swung further Vale's way four minutes after the interval when Millwall's veteran defender Richard Shaw was sent off for a second yellow card - the second for flattening Luke Rodgers.
Vale sensed victory was there for the taking as Danny Glover's powerful shot forced a smart stop from Pidgeley at his near post.
Whitaker twice went close before Lowe leapt above the Millwall defence to bury a firm header from Dave Mulligan's free-kick.
Debutant Mulligan was again the provider in the closing seconds when his left-wing cross found Lowe, who made no mistake from five yards.