Blum and Quintero both went deep during a seven-run fifth inning, in which the Astros also scored a pair of runs on two Washington errors.
The big inning carried Houston to its sixth victory in eight games and made a winner of Bud Norris (9-8), who yielded two runs on six hits and four walks through 6 2/3 frames. He struck out six.
The Astros have logged wins in 10 of Norris's last 11 starts.
Nats starter Livan Hernandez (10-12) allowed all eight runs, but only four of them were earned, due in part to his own throwing error in the fifth.
Adam Dunn drove in a pair of runs with a first-inning single for Washington.