Beaten 5-1 in the reverse fixture on the opening day of the campaign, the Millers hauled themselves back into this game on two occasions, thanks to strike from Jon Taylor and an own goal from Ezri Konsa.
But soon after drawing level in the 73th minute, the Millers conceded straightaway when Mokotjo netted his second of the game and top-scorer Neal Maupay sealed it with a fourth.
Despite showing great character in a strong first-half response after going behind, United were second best in the second half with Brentford showing plenty of quality on the break.
The Millers made one change from the side which were narrowly beaten at Ipswich, with Richie Towell - available again after suspension - coming in for Sean Raggett.
The first half could not have started in more abject fashion for the hosts, with Brentford undressing them down the left to take an early lead through Mokotjo - and the signs looked ominous for the hosts.
It was to their immense credit that they rallied impressively after a fraught opening and the hosts really should have taken in a lead for their exertions at the interval.
A sweet leveller from Jon Taylor from distance after a corner was not cleared restored parity on 20 minutes and while Brentford posted danger on the counter, with Said Benrahma - who set up the Bees' opener - looking particularly threatening, it was the hosts who had the bonafide chances to go in front.
A fine right-wing centre from Zac Vyner was met by Taylor, whose effort flew agonisingly wide before a huge moment in the context of the game.
A terrific cross from Will Vaulks was met by Clark Robertson, whose point-blank header produced a fine reaction save from Daniel Bentley - with Ajayi somehow slicing the rebound wide with the goal at his mercy.
Sixteen-goal striker Maupay almost announced himself on proceedings early in the second half after he prodded just wide from a tight angle after being picked out by a smart pass from Yoann Barbet.
It was a cue to a dominant opener to the half from the visitors and they cashed in with a superbly-manufactured second goal on 53 minutes.
It was started and finished by Benrahma, whose unerring low finish gave Marek Rodak no chance after an exemplary move also involving Ollie Watkins and Romaine Sawyers.
Rotherham's response saw Robertson plant a firm header straight at Bentley, but it was not the prelude to a spell of dominance, with the hosts showing trademark perspiration, but little perspiration.
The hosts needed something and it arrived when a cross on the right was met by Robertson, whose header went in off Bees defender Konsa, but the lead was short-lived.
Brentford swept down the other end and regained their lead after Mokotjo finished off a sweeping move, with the final assist coming from Rico Henry.
Maupay missed a golden chance to seal it when he chipped wide of an empty net after being sent clear before seeing an effort blocked by Rodak.
The French striker finally had his moment when he drilled home a fourth for the visitors late on.
Rotherham United: Rodak; Vyner (Yates 78), Ajayi, Robertson, Mattock; Vaulks; Forde (Vassell 86), Wiles (Crooks 59), Towell, Taylor; Smith. Substitutes unused: Price, Wood, Raggett, Jones.
Brentford: Bentley; Konsa, Jeanvier, Barbet; Dalsgaard, Mokotjo (Da Silva 88), Sawyers, Henry; Benrahma (Canos 76), Maupay, Watkins (Ogbene 88). Substitutes unused: Daniels, Odubajo, McEachran, Sorensen.
Referee: T Harrington (Cleveland).
Attendance: 8,319 (606 Brentford supporters).