Roberto Martinez's men made light work of a Russia side that went into the game on the back of seven consecutive victories in which it had conceded just once.
Coach Stanislav Cherchesov stood and watched as his defence was run ragged by the Hazard brothers and by Dries Mertens and Kevin De Bruyne, who controlled the game from midfield.
Romelu Lukaku scored the final goal of a victory that moves Belgium six points clear at the top of Group I with nine wins from nine games, Russia's consolation strike from Georgi Dzhikiya the only fly in the ointment for Martinez.
Lukaku's feet seemed to get stuck in the turf when Eden Hazard's pull-back found him unmarked in the box early on, but moments later Thorgan Hazard made amends after being played into the box by his older brother.
The Borussia Dortmund winger jinked inside Mario Fernandes before scoring with a clean strike that flew into the top corner of Guilherme's net.
Lukaku's well-judged knock-down presented the unmarked Eden Hazard with a chance to double Belgium's lead from the edge of the box and the Real Madrid man made no mistake, beating Guilherme for power with his clinical low drive.
Russia was pulled apart for the third, which arrived in the 40th minute when Mertens's weighted pass released De Bruyne, who strode through a huge gap in the hosts' defence and drew Guilherme before squaring to Eden Hazard for a simple finish.
Thorgan Hazard played Mertens in for what looked like a certain goal early in the second half but the Napoli man fired tamely at Guilherme before leaving the field clutching his hamstring.
The loss of Mertens did not stop Belgium from chasing a fourth, which came courtesy of Lukaku's surge across the edge of the box and a thunderous low finish from the Inter striker.
Thibaut Courtois could only parry Dmitry Kuzyaev's shot into the path of Dzhikiya 11 minutes from time, but his side-footed shot into the unguarded net did little to take the sheen off a fine Belgium win.
Belgium entertains Cyprus in Brussels on Wednesday (AEDT), while Russia travels to San Marino to face Group I's straggler.