Valtteri Bottas was third and Kimi Raikonnen fourth.
A fifth victory of 2017 for the Briton would put the pressure back on Ferrari's Vettel and Hamilton can celebrate another milestone by bagging pole position on Saturday at the long and fast Spa-Francorchamps circuit.
Starting from P16, the Brazilian overtook the two Force India cars to finish in the points.
Hamilton, a victor twice before at Spa, is now 14 points down on the German in the championship chase.
The three-time F1 champion was already ahead when he went even faster with a final lap for Mercedes, but Ferrari driver Sebastian Vettel limited the damage with a fine lap to join Hamilton on the front row.
"I'm here to deliver a very special message from Corinna Schumacher and the Schumacher family, who want to congratulate you on equalling Michael's record", said Brawn, who worked with Schumacher during the latter's illustrious career. "Really grateful for all the hard work".
"I've had the privilege of racing with him from karting days, and have always admired him".
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"I think the track will suit the Mercedes, as will Monza, so I am optimistic of a good result in both races".
Just five seconds separated the top five drivers, before Hamilton and Vettel pulled away from the pack. It was fun to be racing against another team and Sebastian really at his best and the vehicle at his best, battling within half a tenth every lap. "I remember coming here in 1996, my first grand prix, and watching Michael come by and the engine vibrated my rib cage and that was when my love for the sport took another step".
"He was waiting for me to, I didn't".
"Restart, that time maybe I wasn't entirely happy".
"It's nearly insane to think I've reached Michael's record, a fantastic milestone". I do know we are the best equipped as we've ever been to deal with a scenario like that.
It might be an emotional achievement as the Schumacher family is marking the 25th anniversary of the German's maiden victory, in Belgium in 1992, with son Mick driving the track in his father's 1994 Benetton auto to honor his father's achievements.
Not only did Hamilton manage to level up to Schumacher's pole record but also did it in fewer Grand Prix's than the German legend.