Davies tucked home an 18th-minute penalty after Kevin Nolan was penalised for handball and Lee made it two in the 39th minute after United failed to clear a Matthew Taylor shot that had hit the woodwork.
Elmander scored his seventh of the season in the 50th minute but newly capped England international Andy Carroll reduced the arrears two minutes later.
But Elmander grabbed his second of the game in the 72nd minute before Fabricio Coloccini was red-carded for elbowing Elmander. Davies completed the rout by scoring his second penalty in added time.
The victory moved Bolton up to fourth and Newcastle down to nineth.
PREMIERSHIP
Birmingham 1 Chelsea 0
Arsenal 2 Tottenham 3
Man Utd 2 Wigan 0
Liverpool 3 West Ham 0
Bolton 5 Newcastle 1
West Brom 0 Stoke 3
Blackpool 2 Wolves 1
Birmingham heaped more agony on Chelsea when Lee Bowyer's first-half winner condemned them to their third defeat in four games at St Andrews.
Bowyer latched onto a header from Cameron Jerome to slide the ball home from eight yards in the 17th minute to hand the Blues their second successive loss.
Bowyer's goal came against the run of play and Chelsea were denied an equaliser when Ben Foster produced a fine save to deny Didier Drogba, who also hit the woodwork.
Foster then pulled off a string of fine saves in the second-half to keep Chelsea at bay.
The Blues now lead at the top of the Barclays Premier League only on goal difference over Manchester United.
Sir Alex Ferguson's side took advantage of Chelsea's slip by recording a 2-0 victory over nine-man Wigan at Old Trafford.
Patrice Evra's first goal in three-and-a-half years in first-half injury time and a 77th-minute header from Javier Hernandez earned United all three points to move them level on points at the top with Chelsea.
Wigan's task was made worse by red cards for Antolin Alcaraz and Hugo Rodallega in the space of three minutes in the second half.
First Alcaraz went for a second bookable offence and he was followed by Rodallega, who received a straight for two-footed lunge at Rafael da Silva.
Tottenham completed one of the most amazing comebacks in north London derby history as a 3-2 victory ended their 17-year wait for a win at Arsenal.
The Gunners romped to a 2-0 half-time lead thanks to goals from Samir Nasri and Marouane Chamakh as William Gallas' return to the Emirates looked set to end in defeat.
But Gallas had the last laugh as Gareth Bale pulled a goal back and Cesc Fabregas inexplicably handled Rafael van der Vaart's free-kick to allow the Dutchman to level from the penalty spot.
Then Younes Kaboul headed home a dramatic winner five minutes from time as Spurs moved to within four points of their fiercest rivals.
Blackpool beat Wolves 2-1 thanks to first-half goals from Luke Varney and Marlon Harewood at Bloomfield Road.
Varney slammed a volley into the top corner for a stunning opening goal in the 3rd minute and then Wolves goalkeeper Marcus Hahnemann flapped at a corner to allow Harewood to bundle home a minute before the break. Kevin Doyle scored an 86th minute consolation goal for Wolves.
Three second-half goals, two from the penalty spot, saw Stoke earn their third win in a row with a 3-0 success over West Brom at The Hawthorns.
West Brom goalkeeper Scott Carson brought down Stoke striker Kenwyne Jones inside the box and Matthew Etherington coolly converted the first spot-kick in the 55th minute.
Albion's Simon Cox then fouled Dean Whitehead and substitute Jon Walters fired home the second penalty five minutes from time. Walters then grabbed his second of the game to complete the scoring in added time.
In the late game, Liverpool returned to winning ways in comfortable fashion with a 3-0 victory but their task was made easy by a woeful West Ham side at Anfield.
Goals from Glen Johnson and Maxi Rodriguez, either side of a Dirk Kuyt penalty, were enough to wrap up the points in the first half.
Hammers goalkeeper Robert Green kept the score down with a string of saves as the pressure mounted on manager Avram Grant.