The Deans are second in the Wessex League premier division
They have won nine of 12Â games.
Birmingham praised his side for the way they dealt with difficult opponents on a day when it would have been easy to not be on point.
The Horndean managerÂ said: '˜The conditions were horrendous for everyone out there.
'˜For me the most pleasing thing was the way we kept our shape out of possession.
'˜It is something we worked hard at during the week following our FA Vase exit.
'˜Our decision making was good.
'˜The players identified when to go forward and get on the front foot.
'˜Alresford had plenty of possession but none of it in areas that could hurt us.
'˜When they came at us in the first 15 minutes of the second half we weathered the storm.'
Horndean broke the deadlock five minutes before half-time following some great work from Harry Jackson on the left.
His cross left poacherÂ Zac Glasspool with a simple tap-in at the far post.
After dealing with the early second-half pressureÂ Jack Maloney stretched the lead with an outstanding 20-yard strike.
The goal followed some excellent build-up play involving two quick one-twos on the edge of the area.
After thisÂ Horndean were guilty of conceding a few cheap free-kicks and the home side punished them by reducing the deficit from one of them.
But the team held out to get the job done.
Now they will be looking to keep the momentum going.
Birmingham added: '˜I have to be happy with our position in the league.
'˜The players are level headed, though, and know we face a tough few weeks ahead.'
Fareham TownÂ continued their slide down the league with a resounding 6-0 defeat at Lymington Town.
Reds manager Pete Stiles admitted he feared before the match it wasn't likely to be a good day for the team.
He said: '˜I half expected it because we are so stretched at the moment.
'˜We had 15 players unavailable for one reason or another.
'˜Our goalkeeper Luke Douglas was playing his first game for months.
'˜I thought he did well under the circumstances.'
AFC Portchester'sÂ game at Hamble Club was abandoned after 20 minutes due to a waterlogged pitch.
The Royals were trailing to a 14th-minute goal when the referee deemed the pitch was no longer playable.
In division oneÂ Petersfield TownÂ slumped to a 5-2 defeat at Verwood Town.
Jordan Neal scored both the goals for the Rams.