The Dutchman won from ninth on the grid, after losing out on a shot to set a qualifying time on Saturday after botching his first run, and was denied a further chance by Charles Leclerc's late-session crash.
He was equipped with the hard tyre on a contra-strategy to Perez, who began the race from pole position on the medium compound, and the Mexican made sure to stay ahead of fellow front-row starter Fernando Alonso.
Verstappen initially dropped down to 10th at the start as Valtteri Bottas - starting alongside him on the grid - got a better getaway and leapfrogged the Red Bull and the Alpine of Esteban Ocon.
But the two-time champion settled in, quickly dispatching the brace of cars ahead by the end of the second lap.
Further quick fire passes on Leclerc and Kevin Magnussen, who were embroiled in a delectable scrap over sixth place, got Verstappen closer to the front of the field.
A series of fastest laps in the early stages then continued to bring Verstappen back into play, and he got a tow from Russell with DRS to dive past at Turn 17 on the eighth lap of the race - as the Briton complained of vibrations under braking.
Source: Autosport