The on-loan Chelsea centre back headed home 11 minutes from time to cancel out Shaun Williams's spectacular 30-yard strike in the 61st minute and clinched a third successive 1-1 draw for Blues.
Clarke-Salter's equaliser meant eight of Birmingham's 11 goals scored at St Andrews in the Championship this season have been headed, including the last five.
Birmingham caretaker head coach Pep Clotet has now failed to beat two of his predecessors in five days after Wednesday's 1-1 draw at Sheffield Wednesday.
But at least this time he got a handshake after Garry Monk refused his hand in midweek.
More importantly, Blues are five games without a win, since October 26.
Millwall made it 10 points out of 18 under former Birmingham manager Rowett.
A draw was a fair result with Blues having two penalty appeals turned down while Ivan Sunjic was denied and Jude Bellingham, Lukas Jutkiewicz and Alvaro Gimenez fired wide, while for Millwall, Matt Smith and Ben Thompson were foiled.
The first serious chance arrived in the 29th minute when Sunjic's skidding drive from 25 yards brought a diving save to his left from goalkeeper Bartosz Bialkowski.
Millwall however went closest to breaking the deadlock, 11 minutes before the break.
Trueman was in action again soon afterwards, palming upwards from Thompson's volley from the edge of the box.
The half closed with Millwall going close as Wallace's shot from an acute angle drifted just wide.
Birmingham had a more justifiable shout for a penalty waved aside in the 49th minute when Alvaro Gimenez fell after having his shirt tugged by Jake Cooper. But referee Woolmer was again unmoved.
Jutkiewicz and Gimenez wasted chances for Blues, the former could only roll the ball wide with Bialkowski to beat after being put clean through.
Then Gimenez screwed disappointingly wide from an angle when Maxime Colin's through pass sat up perfectly.
Millwall punished them when Williams curled a spectacular shot into the top corner from 30 yards from Jed Wallace's short pass.
Pressure from Blues resulted in an equaliser when Clarke-Salter glanced home Dan Crowley's outswinging corner at the near post.
With Blues piling forward, Bellingham danced through only to poke his left-footed shot just wide of the far post.