After dropping points at the weekend the two clubs desperately needed a victory but instead remain in mid-table.
Derby loanee Mason Bennett fired the hosts ahead in the first half, but Rhian Brewster’s free-kick forced an own-goal from goalkeeper Bartosz Bialkowski in the 66th minute to earn a share of the spoils for the Swans.
After a shock home defeat to Luton on Saturday, Steve Cooper made three changes and it helped the visitors start brightly in the capital.
On-loan Liverpool forward Brewster caused early problems for Millwall and Conor Gallagher, on loan from Chelsea, went close with a deflected shot after quarter of an hour.
The opener did arrive with 21 minutes on the clock, but it went to Millwall against the run of play after a wonderful counter-attack.
Mahlon Romeo won the ball, Jed Wallace got away on the right and, despite Ben Wilmot sliding in, the ball ricocheted back to the winger and he was able to cut back for Bennett to fire home his first goal since moving to the Den in January.
Swansea almost levelled after a drinks break when Brewster was presented with a good chance from close range, but Lions captain Jake Cooper got back on the line to deflect over in impressive fashion.
Wilmot had to help out his goalkeeper four minutes later when Shane Ferguson threaded a fine ball through to Jed Wallace.
He rounded Freddie Woodman from a tight angle and looked to find the net, but the on-loan Watford centre-back was able to put the ball behind for a corner.
It remained 1-0 until half-time and, even though there were no fans present, the Millwall board and directors were making their support heard from the stands.
Home boss Gary Rowett replaced goalscorer Bennett with Connor Mahoney at the break and chances were more frequent at the start of the second period.
A curled effort by Gallagher tested Bialkowski before Andre Ayew had to get back to prevent Tom Bradshaw from doubling Millwall’s lead.
That would prove crucial for Swansea as they equalised in the 66th minute with a moment of magic from Brewster.
From 25 yards, the Liverpool loanee curled a free-kick over the wall and, although it smashed against the crossbar, hit goalkeeper Bialkowski’s back and went in.
A point did little for either sides’ play-off hopes and Rowett’s men pushed to retake the lead and wanted a penalty when Ben Cabango and Bradshaw collided with 17 minutes to go, but James Linington waved away the appeals.
Murray Wallace should have done better two minutes later when he headed Jed Wallace’s corner wide at the back post.
It was end-to-end when Millwall introduced top goalscorer Matt Smith with five to go, but the crucial final clear-cut chance did not fall to him.
Lions defender Murray Wallace headed against a post from a corner in the 87th minute as the match finished all square.