The 25-year-old, who won Olympic gold over 3000m and 5000m in Vancouver in 2010, had to make do with two seconds over the former distance in Heerenveen and Kolomna last month.
However, as the World Cup circuit travelled to Kazakhstan for round three and the first women's 5000m race was scheduled, Sablikova finally tasted victory with a time of 7:00.75.
Sablikova, who has won the overall 3000m-5000m World Cup title for the past six seasons, edged out Claudia Pechstein by 0.3 seconds while Olga Graf was a further 0.33 back in third.
Victory sees Sablikova become the outright World Cup leader, having previously been level with Stephanie Beckert on 160 points, with 260 with the German, who was fourth, second on 220.
Meanwhile in the men's 1500m American Shani Davis claimed his first win over the distance this season while second for Havard Bokko saw him take the overall World Cup lead.
Two-time Olympic champion over 1000m, Davis posted a winning time of 1:46.01 with Bokko 0.33 behind for second while Zbigniew Brodka was 0.08 further adrift in third.
With Maurice Vriend only managing eighth almost a second shy of Davis, Bokko's second place saw him demote the Dutchman at the top of the overall rankings with his lead at the top 29 points.
Meanwhile the Dutch men's team pursuit trio followed up on their win in Heerenveen to take victory again in Astana after clocking a time of 3:41.27.
Jorrit Bergsma, Koen Verweij and Jan Blokhuijsen combined to edge out Korea by 0.22 while the trio from Norway took third almost another two seconds back.