Valmo Kriisa poured in 14 points and veteran Martin Müürsepp 13 as Estonia won their first additional qualifying round game in Group B at Sweden, 57-50.
The team from the Baltics did just enough to prevail in a battle of cold-shooting teams.
Sweden were just 13 of 36 (36.1%) inside the arc, and four of 26 (15.4%) beyond it, while Estonia shot five of 17 (29.4%) from long range.
From two-point range, Estonia were 13 of 32 (40.6%).
Estonia took the lead for good at 29-28 on Tanel Sokk's lay-up less than four minutes into the second half.
They stretched their advantage to 10 points early in the fourth quarter, but the Swedes battled back and made sure for a thrilling finish.
Fredrik Jonzen's tap-in sparked an 8-0 run that left the hosts trailing 44-42 with just under six minutes to go in the contest.
Kristjan Kangur's tap-in and two free throws by 33-year-old Valmo Kriisa steadied the ship for Estonia, and Sweden got no closer than four points the rest of the way.
The Estonians were better at the free throw line, making 16 of 22 (72.7%) compared to 12 of 18 (66.7%) for the home side.
Both teams grabbed 40 rebounds.
Estonia are back in action on August 13 in Tallinn against FYR Macedonia, while Sweden play again four days later in Skopje.