The Spurs stretched their season-high winning streak to six games with the victory.
The Spurs improved to 6-1 on their nine-game road trip, the longest in franchise history. Things do not get any easier as San Antonio concludes its trek against the Los Angeles Lakers and Sacramento.
"We had a lot of guys step up tonight and this is a huge win," Duncan said. "It's a great way to start (the second half)."
The matchup of the league's hottest teams lived up to its billing. After forcing overtime on two free throws by Scottie Pippen with 1.3 seconds left, the Blazers took a 111-109 lead on Pippen's jumper with 1:39 remaining in the extra session.
Rookie Emanuel Ginobili then hit a three-pointer, giving them a 112-111 lead with 42 seconds to go.
On Portland's next possession, Pippen lost control of the ball on a drive to the basket, but Duncan gave the Blazers another chance by missing two free throws with 10 seconds left.
Portland's hopes ended when Pippen missed a trey with five seconds remaining. Parker made two more from the line for the final margin.
"Both teams competed really well and I guess if it were to have continued, each team would have continued to make shots," said Spurs
Coach Gregg Popovich. "Luckily, the clock ran out after we made some shots."
San Antonio, ranked 25th in the NBA in free-throw shooting, feasted at the line, making 34-of-39 attempts.
"It was a heck of a game," said Portland Coach Maurice Cheeks. "Unfortunately, we had to lose it. It was a playoff atmosphere. I think this is how our games are going to be from now on."
Rasheed Wallace scored 25 points before fouling out for the Blazers, who lost for only the sixth time in their last 28 games.