Bergkamp had reached the 100-goal mark in the FA Cup tie against Oxford United a week ago and Henry’s two goals against the Blues enabled him to reach that milestone in his 181st appearance for the Gunners.
It was a thoroughly convincing display by Arsene Wenger’s side as they clinically disposed of the Premiership new boys to move clear again of second-placed Manchester United.
They cut through the home defence almost at will with, not for the first time, the guile of Bergkamp and the pace and power of Henry an unstoppable combination.
Manager Arsene Wenger saluted Henry and said: “Henry was exceptional today. For him and Dennis to both reach the 100-goal mark in the space of a week shows they are two exceptional strikers.
“The exception becomes the norm with him. I think he is a fantastic striker. He’s only 25 and has played just three years in this position.
“But what I like about him is that he is not only a goalscorer but also a team player who provides chances for other players as well.”
Wenger flashed a warning to the rest of the Premiership by insisting that his side were getting back to their best.
He said: “I enjoyed the team performance. There was a good passing game and sharp movement. You could see that we were refreshed after the break some people had.
“Maybe we were fortunate to score first and we suffered a few moments of anxiety with the long ball but we always looked in control. Once we scored the third goal, the game was over and we could have scored a few more. I am very pleased because it looks like our fluent game is coming back and that can only be good for us.”
But City will take some consolation from the debut of Christophe Dugarry who posed questions of the Gunners defence but had little support.
After a 25-minute delay caused by a power failure, the game was finally able to get underway at 4.30pm and Arsenal quickly made up for lost time.
The first chance fell to the Gunners after Bergkamp found Sylvain Wiltord in space with a reverse pass but he volleyed his shot across the face of Nico Vaesen’s goal.
At the end Dugarry was only just off target with a first-time effort following a cross from Robbie Savage.
But after six minutes the Blues defence was ripped open as Henry tucked away his 19th goal of the season and 99th in total for Arsenal.
Bergkamp again was the driving force behind another move which saw Henry side-foot his shot wide when well placed following a cut-back across the area by Robert Pires.
Ferdinand Coly, who was making his home debut, became the first player to be yellow-carded for a challenge on Edu and then Jamie Clapham forced David Seaman into a low save away to his left.
But the impression was that Arsenal could step up a gear anytime they wanted and after 29 minutes a superb strike from Robert Pires doubled their lead.
Michael Johnson and Wiltord tussled for the ball and Johnson failed to get any power into his clearing header which fell to Pires who volleyed an unstoppable shot past Vaesen from 18 yards.
Dugarry offered the main ray of hope for the home side and Lauren was booked for a foul on the World Cup winner.
Birmingham had to strike early in the second period if they were to have any chance of getting back into the match and there was certainly more purpose about their play.
Dugarry was at the centre of most of their most promising moments and he had one powerful show blocked by Ashley Cole. Then Martin Keown was yellow-carded after 59 minutes for bringing down the Blues striker.
Then two goals in three minutes put the game firmly out of Blues reach. After 67 minutes Vaesen only punched a corner from Edu into the path of Bergkamp some 30 yards from goal.
He calmly crossed the ball back into the area and Lauren made no mistake with a looping header into the roof of the net.
Then came Henry’s moment of glory which took him to the 100-goal mark as he calmly drilled a low shot past Vaesen following good play by Pires and Wiltord.
Henry came close to completing his hat-trick with a curling effort from 20 yards which flew inches wide.
Dugarry got a standing ovation from the home fans when he was substituted five minutes from time.
BIRMINGHAM: Vaesen, Coly (Grainger 68), Vickers, Michael Johnson, Kenna, Damien Johnson, Savage, Clemence (Devlin 68), Clapham, John, Dugarry (Kirovski 85).
ARSENAL: Seaman, Lauren, Keown, Campbell, Cole, Wiltord, Edu (van Bronckhorst 75), Silva, Pires (Toure 79), Bergkamp (Jeffers 78), Henry.
Referee: S Bennett (Kent).