In the past 18 months, authorities in the South Caucasus nation have arrested dozens, dispersed anti-government rallies and adopted laws curbing freedom of speech and assembly, the organisation said in a report.
Azeri authorities could not be immediately reached for comment, but Baku has repeatedly denied abusing human rights in the past.
"Prosecuting people who criticise the authorities and report on issues of public interest is a cynical and transparent attempt to stifle government critics," HRW researcher Giorgi Gogia said.
The European Union and other bodies in June accused the ex-Soviet state of tightening curbs on free expression by making defamation over the internet a criminal offence punishable by imprisonment.
HRW said authorities had in particular targeted youth activists critical of the authorities on social networks.
Several members of opposition youth movement NIDA were arrested earlier this year accused of plans to instigate violence during protests, and a number of journalists and rights workers were detained on fake charges, it said.
"The authorities have used a range of trumped-up criminal charges, including narcotics and weapons possession, hooliganism, incitement, and treason to lock up these critics."
According to the report, Azeri authorities have also increased fines for unsanctioned protests by up to 100 times and expanded from 15 to 60 the maximum prison term for public order misdemeanours often used to jail protestors.
Western powers are generally critical of Azeri human rights violations, the report said, but the reported abuse has not had a major impact on their relations with Baku.
"That is perhaps due to Azerbaijan's geostrategic importance and hydrocarbon resources," HRW said.
The mainly Muslim Caspian Sea nation, ruled by Ilham Aliyev since he succeeded his father in 2003, has been courted by Western powers because of its role as an alternative to Russia in supplying oil and gas to Europe.
Aliyev, 51, is almost certain to win the upcoming October polls in a tightly controlled political system, despite mounting opposition from Azeris tired of his rule.
Vote monitoring groups have previously criticised the democratic credential of ballots in the country over the past decade.