It was a much-needed three points at The Den for the Swans, who had lost their previous four matches without scoring to leave their Championship automatic promotion hopes in tatters.
But their confidence returned once Andre Ayew had scored their first goal in 500 minutes of football just before the break, as Steve Cooper's side consolidated their place in the play-offs, while all-but ending Millwall's slim top-six ambitions.
The Swans were struggling to get it together in the final third, with passes not reaching their intended target.
Coming close seemed to spur the visitors on, but a promising counter-attack fizzled out when Lowe over-hit a through ball meant for Ayew.
However, Swansea's goal drought finally came to an end on the stroke of half-time, as Conor Hourihane helped the ball on for Ayew, who bent a superb shot beyond Bialkowski into the far corner.
Their lead was almost cancelled out within a minute of the restart as Cooper's header from Scott Malone's cross came back off the inside of the post.
Fresh from surviving that scare, the Swans nearly doubled their lead when Ayew poked the ball through for Wayne Routledge, whose rising effort was beaten away by Bialkowski.
However, Swansea took a huge step towards sealing the points in the 76th minute when Lowe ran on to a smart pass by Routledge and progressed into the area before crashing in his first goal in 18 matches.
Zohore almost forced a grandstand finish when his terrific shot on the turn was superbly tipped over by Woodman.
But the Swans added a third with five minutes to go when Ayew's cut-back found Lowe in space and he calmly lifted the ball into the top corner for his second.