That saw Verstappen pit for the first time on Lap 10, and then again on Lap 29, making for a 26-lap run to the flag on a set of hard tyres.
Having gained the lead at the start, Hamilton swapped his medium tyres to the hards on Lap 13, giving up track position in the process by way of the undercut.
He then remained on track until Lap 37, giving him an eight-lap tyre delta over Verstappen in the run to the flag, and a 6.7-second deficit to chase down.
Ultimately, while able to close on the leading Red Bull, the seven-time champion was never close enough to consider a move to claim top spot.
“It was such a such a tough race,” Hamilton said.
“[I] Got a good start, gave it absolutely everything, but at the end of the day they just have the upper hand this weekend and we couldn't really ask for more.
“But a big thank you to my team for great pitstops, great hard work throughout the weekend.”
The result was something of a reversal of fortunes from the form shown by Mercedes in Free Practice 1, in which Hamilton and team-mate Valtteri Bottas enjoyed a near one-second advantage.
Hamilton now sits 12 points behind Verstappen in the championship battle with five races to run.
Sergio Perez finished third for Red Bull, meaning Mercedes' constructors' advantage has also been eroded to the tune of 13 points, the difference now just 23 points.
F1 next heads to Mexico for the first round of its third triple-header of the season, the Sao Paulo and Qatar Grands Prix to follow in quick succession.
The Mexico City Grand Prix takes place on November 5-7.