Casemiro put United ahead in the early stages at Old Trafford and Sesko doubled their lead before the interval.
Mathias Jensen’s late strike couldn’t stop United cementing their grip on third place in the Premier League.
They are 11 points clear of sixth-placed Brighton, with the top five guaranteed to reach next season’s Champions League.
Michael Carrick’s side need just two points from their last four matches to ensure their return to Europe’s elite club competition for the first time since 2023-24.
On Sunday, United host bitter rivals Liverpool, who sit three points behind them in fourth, in a clash that will go a long way to deciding who finishes third.
Interim boss Carrick, who replaced the sacked Ruben Amorim in January, is still waiting to discover if he will land the United job on a permanent basis.
The former United midfielder has made a strong case by steadying the ship after Amorim’s turbulent reign.
Leading United into the Champions League would be another persuasive argument as co-owner Jim Ratcliffe considers his options.
A 1-0 win at Chelsea in their previous match had reinvigorated United’s top-five charge after a home defeat against Leeds and a draw at Bournemouth.
Brentford last won at Old Trafford in 1937 and they paid the price for a slow start on their latest fruitless visit.
Casemiro strikes again
Kobbie Mainoo scythed through the Brentford defence with a superb run in the second minute, but Amad Diallo wasted the chance with a close-range shot that was cleared off the line by Sepp van den Berg.
Harry Maguire was inches away from marking his return from suspension with a goal when the United defender’s towering header was clawed off the line by Brentford keeper Caoimhin Kelleher.
United’s pressure was rewarded in the 11th minute as Casemiro finished off a well-worked corner routine.
Bruno Fernandes whipped the set piece to Maguire and his looping header evaded a gaggle of Brentford defenders at the far post as Casemiro rose highest to head home from an acute angle.
Casemiro’s fourth goal in his last six games underlined the enduring value of the veteran Brazil midfielder, who is set to leave when his contract expires at the end of this season.
He celebrated by kissing the badge on his shirt as United fans implored him to stay by chanting “one more year”.
Michael Kayode nearly silenced the love-in with a header that United keeper Senne Lammens pushed away at full stretch.
Igor Thiago’s muscular power was a thorn in United’s side but the Brazilian couldn’t finish, scuffing one chance under pressure from Diogo Dalot before Kelleher saved his close-range drive.
Ayden Heaven’s last-ditch attempt to deny Thiago almost ended in an own goal, but Lammens spared the United teenager’s blushes with a fine save.
United took advantage of those misses to double their advantage in the 43rd minute.
Diallo’s determination to win a tackle deep inside his own half started the move before Fernandes drove towards the Brentford area, slipping a pass to Sesko, who lashed home from 10 yards.
Fernandes has 19 assists this season as he chases the Premier League record of 20 in a single campaign set by Thierry Henry and Kevin De Bruyne.
United were less dominant in the second half and Jensen whipped an eye-catching curler past Lammens from 20 yards in the 87th minute to set up a tense finale.
Carrick’s men wobbled but just about held firm as Mikkel Damsgaard’s header was clutched by Lammens in stoppage time.