Salt was then rubbed into the wounds for Birmingham as Cheikh N'Doye was sent off in the 94th minute following an altercation with Mile Jedinak.
Albert Adomah put Villa in the lead before Hourihane added the second in the 81st minute.
Calderwood, standing in for the indisposed Steve Bruce, was full of praise for the all-round team performance.
Steve Bruce's men earned their seventh win in a row to move into the automatic promotion spots, with Hourihane sealing the win with a stunning effort.
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The storm's impact may also be felt in the low-lying Ha'apai group, where damaging winds, rain and storm surge are likely. Tonga's Fua'amotu Weather Forecasting Centre warned residents could expect "very destructive hurricane force winds".
'But after we scored we really took control of the game.
Bruce had to contend with the passing of his father, Joe Bruce, on Tuesday and has also had to care for his mother who has been battling illness. He picked his team and picked his subs.
"We are certainly enjoying the elation of beating Birmingham on derby day as the players are very focused on the future".
Villa's domination, undoubtedly generated by the outstanding skill of Grealish, was rewarded with two second-half goals from Adomah and Hourihane.
Adomah may have turned the game in Villa's favour but his team-mate Jack Grealish was the driving force for the hosts.