Day pegged two of the holes back on the seventh and eighth and then the Canadian tied the match on the 15th with a birdie before taking the lead with a crisp iron into the par three 16th which led to another birdie.
They stumbled on the 17th when DeLaet missed a short putt but Day's heroics on the last ensured the full point.
South African duo Charl Schwartzel and Louis Oosthuizen were the other International duo to earn an outright point for their side, defeating Phil Mickelson and Keegan Bradley 2&1.
Two down through seven, the South Africans came back strongly to get another vital win.
Adam Scott and Japanese rookie Hideki Matsuyama never led in their match but grabbed a half point after the 20-year-old Matsuyama had a tap-in birdie on 18 that saw things all square with Bill Haas and Webb Simpson.
The match was an absolute belter with both sides 11-under on the round.
Down two with four to play, Scott holed out a chip shot for eagle on the 15th before Matsuyama made birdie on 16 to draw level.
Like the Day/DeLaet team before them they dropped the 17th but the rookie showed nerves of steel to clinch the half on the last.
Marc Leishman's Presidents Cup debut didn't go the way he would have liked as he and Argentine partner Angel Cabrera were destroyed 5&4 by world No.1 Tiger Woods and Matt Kuchar.
- AAP