The Mercedes driver started in pole position, but was challenged by Ferrari's Charles Leclerc.
After the safety car came out with a couple of laps left to run, Russell was forced to defend his lead again.
"Very strategic driving, it's not easy to overtake here," Russell told Sky Sports.
Hamilton finished third; Ferrari's Charles Leclerc took second place.
Red Bull's Max Verstappen, who had a tough start to the year, finished ninth and without points.
The Chinese GP is on Sunday, with young Kimi Antonelli starting in pole position. The 19-year-old Italian was fastest in qualifying, just over two tenths ahead of team-mate Charles Leclerc.
