The Wizards had lost their first 12 games of the campaign to establish a franchise record for worst start to a season. The all-time NBA record for consecutive losses to start a season will remain in the hands of the Brooklyn Nets, who as the New Jersey Nets began with 19 straight three years ago.
Washington appeared to be cruising to a victory when it built a 79-64 lead with 8:56 remaining, but the Trail Blazers then ran off 15 straight points to tie it.
The game was knotted at 82-82 when LaMarcus Aldridge fouled Okafor and the Washington center hit both free throws.
Portland then missed its final two shots and the Wizards survived despite turning the ball over twice in the final 30 seconds.
Nicolas Batum and Damian Lillard both had 20 for the Trail Blazers, who have lost three straight.