But from the off it was Watford's forwards who dominated. The first real chance came after 22 minutes but Deeney could only head wide Abdi's corner from six yards.
However, Birmingham did not heed the warning and 15 minutes later midfielder Nathaniel Chalobah flicked the ball out to the right for Anya. His cross found Deeney unmarked and six yards out and he made no mistake with his header.
The scoreline was doubled minutes before half-time as the lively Anya drilling an effort straight through Jack Butland, who will be disappointed not to have dealt with the shot.
Watford are the top-scoring team in the Championship, their 64 goals this season six better than nearest rivals Crystal Palace.
A chorus of boos rang round St Andrew's at half-time, but Blues did not improve after the interval and Watford made it three on the hour as Anya squared for Deeney to convert.
Watford were coasting but there was still time for Abdi to add a fourth in the closing stages after Butland could only parry Cristian Battocchio's effort to the edge of the area.
Birmingham manager Lee Clark:
"Watford have some very good players, they're a good team.
"Technically they are some of the best in the division.
"I think the difference between the two teams was in both final thirds."
Watford manager Gianfranco Zola:
"It was a very good result, a good performance.
"I think there were some spells in the game which we were really good, I rate it one of the best performances considering the [injury] difficulties we had.
"But I do think we've played some better games than this."
Full Time The referee signals the end of the game.
Peter Lovenkrands concedes a free kick for a foul on Cristian Battocchio. Free kick taken by Sean Murray.
Wade Elliott concedes a free kick for a foul on Nathaniel Chalobah. Nathaniel Chalobah takes the direct free kick.
88:19 Goal scored
Goal! - Almen Abdi - Birmingham 0 - 4 Watford Goal scored by Almen Abdi from just outside the penalty area to the top right corner of the goal. Birmingham 0-4 Watford.
Foul by Peter Lovenkrands on Manuel Almunia, free kick awarded. Manuel Almunia takes the direct free kick.
Corner taken by Nathan Redmond from the left by-line played to the near post, clearance by Marco Cassetti.
Free kick taken by Manuel Almunia.
Substitution Matej Vydra leaves the field to be replaced by Jonathan Hogg.
Wade Elliott concedes a free kick for a foul on Nathaniel Chalobah.
Booking The referee shows Peter Lovenkrands a yellow card for dissent.
Peter Lovenkrands takes a shot. Save made by Manuel Almunia. Corner from the left by-line taken by Nathan Redmond, Manuel Almunia makes a save.
Effort from inside the area by Curtis Davies misses to the left of the target.
Substitution Ikechi Anya goes off and Sean Murray comes on.
Nathan Redmond has a headed effort at goal from close in which goes wide left of the goal.
The offside flag is raised against Wes Thomas. Manuel Almunia takes the free kick.
Effort on goal by Matej Vydra from deep inside the area goes harmlessly over the bar.
Substitution Mitch Hancox on for Paul Robinson.
Substitution Adam Thompson on for Daniel Pudil.
Inswinging corner taken by Almen Abdi from the left by-line, comfortable save by Jack Butland.
Ikechi Anya provided the assist for the goal.
61:36 Goal scored
Goal! - Troy Deeney - Birmingham 0 - 3 Watford Troy Deeney gets on the score sheet with a goal from close in to the top left corner of the goal. Birmingham 0-3 Watford.
Substitution Robert Hall leaves the field to be replaced by Nathan Redmond.
Short corner taken by Almen Abdi from the left by-line.
Paul Caddis gives away a free kick for an unfair challenge on Ikechi Anya. Manuel Almunia takes the free kick.
Inswinging corner taken left-footed by Robert Hall from the right by-line. Corner taken by Robert Hall from the left by-line, clearance made by Marco Cassetti.
Inswinging corner taken right-footed by Almen Abdi from the left by-line, save by Jack Butland. Outswinging corner taken right-footed by Matej Vydra, Jack Butland makes a comfortable save.
Robert Hall takes a inswinging corner to the near post, Matej Vydra manages to make a clearance.
Peter Lovenkrands takes a shot. Nyron Nosworthy gets a block in. Outswinging corner taken from the left by-line by Robert Hall, save by Manuel Almunia.
The referee gets the second half started.
45:00 +1:35 Half time
Half Time The ref blows to end the first period.
The assistant referee flags for offside against Christopher Burke. Indirect free kick taken by Manuel Almunia.
42:56 Goal scored
Goal! - Ikechi Anya - Birmingham 0 - 2 Watford A goal is scored by Ikechi Anya from close range to the bottom right corner of the goal. Birmingham 0-2 Watford.
Free kick awarded for a foul by Steven Caldwell on Troy Deeney. Direct free kick taken by Nathaniel Chalobah.
Assist on the goal came from Ikechi Anya.
37:16 Goal scored
Goal! - Troy Deeney - Birmingham 0 - 1 Watford Troy Deeney finds the net with a headed goal from inside the six-yard box. Birmingham 0-1 Watford.
Effort on goal by Wes Thomas from just inside the penalty area goes harmlessly over the target.
Ikechi Anya challenges Robert Hall unfairly and gives away a free kick. Free kick crossed left-footed by Robert Hall from left wing, save by Manuel Almunia.
Corner taken left-footed by Robert Hall, Troy Deeney manages to make a clearance.
Free kick awarded for an unfair challenge on Morgaro Gomis by Cristian Battocchio. Free kick crossed by Robert Hall, Nyron Nosworthy makes a clearance.
Peter Lovenkrands gives away a free kick for an unfair challenge on Daniel Pudil. Strike comes in from Matej Vydra from the free kick, Jack Butland makes a save.
Corner taken by Almen Abdi from the left by-line played to the near post, clearance by Curtis Davies.
The referee blows for offside against Matej Vydra. Jack Butland takes the free kick.
Almen Abdi takes a shot. Jack Butland makes a save.
Inswinging corner taken by Robert Hall from the right by-line, Nyron Nosworthy makes a clearance. Free kick awarded for a foul by Morgaro Gomis on Cristian Battocchio. Free kick taken by Manuel Almunia.
Matej Vydra takes a shot. Jack Butland makes a save.
Matej Vydra takes a shot. Steven Caldwell gets a block in. Almen Abdi takes the inswinging corner, Close range header by Troy Deeney misses to the right of the target.
Effort on goal by Matej Vydra from a long way out goes over the bar.
Nathaniel Chalobah takes the free kick.
Booking Paul Robinson goes into the referee's book for unsporting behaviour.
Free kick awarded for a foul by Paul Robinson on Almen Abdi.
The ball is crossed by Christopher Burke, Lloyd Doyley makes a clearance.
Morgaro Gomis has an effort at goal from long range that goes wide left.
Wes Thomas takes a shot.
Ikechi Anya takes a shot. Save by Jack Butland.
Wes Thomas challenges Nathaniel Chalobah unfairly and gives away a free kick. Nathaniel Chalobah takes the direct free kick.
Corner taken by Almen Abdi from the left by-line, clearance made by Steven Caldwell.
Wes Thomas concedes a free kick for a foul on Ikechi Anya. Free kick taken by Marco Cassetti.
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