Wallace scored the only goal on the counter-attack on 71 minutes, the first shot on target for either side in a drab match at Pride Park.

A swift break after a poor Rams free-kick saw Shane Ferguson release Wallace, who scored with a fine left-footed shot from the edge of the box.

Derby, who remain one place and two points outside the play-offs but have now played a game more then sixth-placed Bristol City, did not manage their first effort on target until the 92nd minute.

Lions goalkeeper Jordan Archer had to make a fine stop to keep out Fikayo Tomori's header in a frantic finish.

But Millwall held on for a second away Championship win this season to move up to 19th in the table, five points clear of the relegation zone.

• Relive Millwall's victory over Derby

Boos could be heard ringing around the ground following a poor display by the home side, which means they have won just once in four league matches.

The club's recent past has seen them lose form in the second half of the season and miss out on promotion despite being well placed - and a performance lacking creativity and a cutting edge will have done nothing to allay fears of that trend repeating.

But an intriguing set of fixtures over the coming weekend will bring plenty of hope of returning to the top six.

By the time the Rams travel to face fierce rivals and fellow play-off hopefuls Nottingham Forest at the City Ground on Monday, Bristol City will have played away at leaders Norwich City and West Bromwich Albion, in fourth, will have hosted second-placed Sheffield United.

Frank Lampard has lost nine of 32 league games as Derby boss

Derby County manager Frank Lampard told BBC Radio Derby:

"We knew it would be tough because Millwall make it difficult for you. They defend deep and they are very organised.

"They stop the game a lot. They play long balls into the box and they are very effective with what they do.

"But we didn't have enough on the ball to win the game. Our quality wasn't good enough.

"There were no surprises in the way Millwall set up but when we had opportunities to move the ball quickly and get it wide we fell slightly short, which made it a frustrating evening."

Millwall manager Neil Harris:

"I sensed that sparkle back about us again - that doggedness and clean-sheet mentality has been there for a few games now.

"I talked to the players about having belief and that clinical edge.

"We have not scored a lot of goals recently in the league so when those moments do come along, you have got to take them.

"It was a great counter-attacking goal but the all-round defensive display is up there with one of the best while I have been in charge. The disciple to stick to the game-plan was first class."