But they had Andy Marshall and the officials to thank after Norwich City enjoyed much the better of the second half.
The Lions went ahead midway through the first period, but Dean Ashton should have put the home side level when he headed over from Darren Huckerby's left-wing cross.
Millwall had gone in front as Ady Williams rose to head home Jermaine Wright's cross after Jody Morris' initial corner had been cleared by the home defence.
Seven minutes into the second half Ashton made amends with a header from Jurgen Colin's right-wing cross that crossed the line before Calum Davenport made sure by blasting the ball into the back of the net.
Referee Taylor and an assistant then missed a blatant push on Davenport in the Lions penalty area before Darren Huckerby did earn a penalty when he was pushed over by Jamie Vincent.
Marshall dived to his left to palm away Huckerby's right-foot spot-kick and the Millwall defence cleared the danger.
Norwich fans thought their team had taken the lead when Gary Doherty headed the ball into the Millwall goal with minutes remaining, but their joy was cut short when Mr Taylor awarded a free-kick to Millwall.
Adam Drury was unlucky to see his goalbound header cleared off the line by Vincent.
Five minutes of added time failed to produce the three points for Norwich which they probably deserved on their second-half comeback.