Murray, the top seed at the tournament, took the opening set as a solitary break proved sufficient, before Berrer saw his serve breached on two occasions to lose the second in more convincing fashion.
The Brit will be the overwhelming favourite to clinch a 19th career title as he sealed his place in the quarter-finals of the Thailand Open.
Berrer had no hesitation in electing to serve first after having won the toss, and the German got on the scoreboard immediately with a composed hold.
WTA Washington
Kyrgios sets up Nishioka final at Citi Open, Norrie loses to Medvedev in Los Cabos
But Murray broke serve at the second opportunity, drilling a succession of fierce groundstrokes to stun his opponent and seize the initiative to assume a 3-1 advantage in the third game.
Murray was utterly unerring on his serve throughout, and closed out the opening set clinically to take it 6-4 with the world number 88 unable to muster a response.
The second half was a near-replica as Berrer opened his account with a solid service hold, only to be broken again in the third game as Murray assumed complete control of the clash once more.
The 31-year-old German flung himself around the court, desperate to exert his presence on the encounter, but Murray outfoxed the German with his guile and touch around the court.
Berrer grew increasingly frustrated with his inability to penetrate with powerful blows from the back of the court, and his blunt approach played into the Brit's hands.
Murray broke again to take a 5-2 lead and move to within a game of the match, before serving out the subsequent game to love to close out victory in unwavering fashion.
It was an entirely ruthless performance from Murray, who did not let his level drop at any stage in the match against an opponent who strived and strained, but ultimately to no avail.
The top seed will next take on Bulgaria's Grigor Dimitrov in the quarter-finals after he overcame Simone Bolelli of Italy in straight sets, 7-6 6-1.
Gael Monfils was another to seal his progression through to the last eight, but the Frenchman found it tough going as he was taken to three sets by Santiago Giraldo.
Monfils took the opening set 6-4 with a single break of serve, before Giraldo reversed the scoreline in the second with a gutsy response to thwart his opponent.
The second seed only conceded a solitary game in taking the deciding set 6-1, and will next face the challenge of Jarkko Nieminen of Finland.
Donald Young took the opening set of his match with Guillermo Garcia-Lopez 6-1, but proceeded to lose the second on a tie-break as the Spaniard found an extra gear.
Young was pushed to 5-5 in the third set, but the American held his nerve to ruthlessly break his opponent and serve out to take it 7-5 and set up a match with Go Soeda of Japan, who beat Tobias Kamke of Germany 6-2 7-6 in their second-round clash.
The fourth quarter-final sees Gilles Simon of France take on Germany's Matthias Bachinger after the pair defeated Yen-Hsun Lu and Danai Udomchoke, respectively on Wednesday.
Highlights: Kyrgios sees off Ymer in straights to reach Citi Open final
Norrie sets up Mexico final against Medvedev after seeing off Auger-Aliassime