Aliyev's late father Heydar ruled the republic for the better part of three decades before Ilham replaced him in a controversial presidential election in 2003. Heydar Aliev died soon afterwards at age 80.
Police officials justified their use of force by branding the opposition "provocateurs" who had tried to stay on the square in violation of public order.
"They were calling for disobedience ... we warned them," Baku deputy police chief Yashar Aliyev said, adding that 29 people had been arrested.
But the US, accused by the opposition of toning down criticism of Azerbaijan because of its oil interests here, was quick to condemn the police action as an "unjustified and unprovoked use of force."
Opposition leaders have already called for another rally.
The Tahirov family at least, said they would be among those attending.
"I feel like its my fault my family members are getting hurt," Tahirov said, "but I will go and fight for my rights."