Monique Currie scored 16 points - all on free throws - for Washington (12-13). The Mystics have won three in a row and five of six.
"Survive and move on," coach Mike Thibault said. "The good part is in 10 days, (looking at the) standings, nobody will remember how or why, just that we survived."
Survive they did. The Mystics entered the fourth quarter leading by 15 points and proceeded to miss their first 12 field-goal attempts of the period.
Tulsa (8-17) closed to 70-69 with 2:20 remaining by outscoring Washington 17-2. Skylar Diggins scored 19 points for the Shock, who have lost 10 of their last 12 games.
The Mystics, who made 26 of 32 free throws overall, countered with four straight from the line. Kara Lawson's jumper, their first basket of the period, came with 45.9 seconds left and gave Washington a 76-71 lead.
"I don't know if I've ever been in a game where (we) won with one field goal in the fourth quarter," Thibault said. "Interesting game. You guys ask the questions. I don't even know where to start."
Tulsa coach Fred Williams' postgame take focused on "missed opportunities" in the final minutes. The Shock had 10 offensive rebounds in the fourth quarter, but converted them into only one second-chance point.
"We had four of five rebounds there at the end to maybe put us up one or so." Williams said after Tulsa's third straight loss by five points or less.
"There are no moral victories on this team, but we're not getting blown out," Diggins said. "We just got to be professionals, try to get better and get ready for the next opponent."
Washington's Monique Currie scored 16 points - all on free throws -- to set a WNBA record for most points without a field goal.
"Yes! I'm in the record book, somehow," Currie exclaimed.