Moore made two free throws with 11.8 seconds for the last of her points in Minnesota's 94-93 victory over the Shock on Friday night.
Moore also had 13 rebounds for Minnesota (3-0), which nearly lost after holding a 16-point lead.
Moore, the MVP of the WNBA Finals last fall, has topped 30 points in every game this year and leads the league in scoring with a 35.0 average.
''It's just being another year older, having another year of experience,'' said the 24-year-old Moore, in her third season. ''And my offseason training, just continuing to be efficient and sharp, just keeping my body in the best shape that I can, on the court and with my nutrition. I'm constantly looking to be aggressive.''
Semione Augustus added 23 points to help the Lynx win their eighth straight in Tulsa and 15th in their last 16 games against the Shock.
Skylar Diggins led Tulsa (0-2) with 21 points, while six others had at least 10.
The Lynx led 35-21 after one quarter, setting a franchise record for points in the opening period, and pushed their advantage to 16 early in the second. They led 60-48 at halftime and held a big lead deep into the third quarter before the Shock battled back.
Minnesota led 80-69 with 43 second left in the third quarter, but Tulsa responded with an 11-2 run to pull within two 3:20 into the fourth. After the Lynx took a six-point edge with 6:24 left, Tulsa scored nine straight points, taking its first lead at 89-88 on rookie Odyssey Sims' lay-up with 3:51 left.
''We were obviously really good on offense while we had our lead,'' Lynx coach Cheryl Reeve said. ''We weren't defending very much in that stretch, we were just outscoring them. And it caught up to us, where we started missing shots, which is going to happen. That allowed them to take the lead and we were very fortunate to hang in there and get a stop at a crucial time.''
Diggins made it 93-90 with 1:04 to go, but Minnesota's Janel McCarville hit a 15-foot jump shot with 46 seconds left and Moore's free throws pushed the Lynx back ahead by one with 11.8 left.
''Janel hit a big jumper and I was just trying to be aggressive and get to the free-throw line and knock them in,'' said Moore, who had 19 points in the first quarter and 28 at halftime. ''Every free throw that I shoot is important, so I just relaxed and shot it just like I shot a million other free throws. I'm just glad it went in.''
Diggins had one more shot attempt just before the final buzzer, but it fell short.
''I don't know what was happening behind me, but that was my only option, to put the shot up, to at least give us a chance,'' said Diggins, who went 2 for 5 from the free throw line and blamed her misses for the loss.
''They're the best team in the league. We fought hard, we didn't lay down to a great team with a lot of veterans that have been together for a long time, and you have to credit them for being able to finish defensively. But we don't have moral victories here, we wanted to win the basketball game.''