Hodgkinson timed 1min 56.72sec for victory, with Ethiopian Tsige Duguma claiming silver in 1:57.15 and Kenya's Mary Moraa taking bronze (1:57.42).
The 22-year-old Briton, who won silver in the Covid-delayed Tokyo Games three years ago, and is also a two-time world silver medallist, held her nerve perfectly at the bell.
The chasing field was closely packed, Moraa on her shoulder all the way around the far straight, before launching an attack with 200 metres to go.
Hodgkinson showed all her nervy steel to hold her off and even put in a spurt to give herself some breathing space.
Moraa was eventually overtaken by Duguma at the line.
Hodgkinson becomes the third British woman to win Olympic 800m gold after Anne Packer in 1964 and Kelly Holmes in 2004.
