Siena trailed 17-11, then used a 12-0 run to pull ahead for good. The Saints opened the second half with a 13-2 spurt to lead 43-27 with 15:52 to go.
The Midshipmen (2-1) got within four at 60-56 with 48 seconds remaining. Downey then made two foul shots and Rob Poole was 3 of 4 from the free-throw line in the final 39 seconds to seal the win.
The Saints played the last 13 minutes with what amounted to a six-man rotation after point guard Evan Hymes cramped up and did not return. Owen Wignot, who suffered a head injury when he crashed to the floor following a driving layup, played only 6 minutes.
J.J. Avila scored 19 points to lead Navy.