The Cardinals were trailing 4-3 with one out in the ninth when Beltran connected for a solo homer into the right field bleachers against Chicago closer Carlos Marmol.
Then in the 10th, Mike Carpenter and pinch-hitter Bryan Anderson each drew a two-out walk off Jaye Chapman (0-1), and Jay followed by smacking a pitch down the first-base line for a double, sending Carpenter home with the decisive run.
The Cards extended their lead for the second National League wild-card spot to 2 1/2 games over Milwaukee with the win and the Brewers' loss to Washington Saturday.
DeJesus hit a solo homer for the Cubs.
Swim Week Miami Beach 2014 [PHOTOS]