The Etixx-QuickStep rider covered the time trial at the Lusail motorsport circuit in 14min 3sec to beat Cancellara (Trek Factory Racing) by eight seconds and world champion in the discipline Wiggins (Sky) by 9sec.
Terpstra's reward was to inherit the leader's gold jersey in the race he is aiming to win for the second successive season.
He has an 11sec advantage over Maciej Bodnar (Tinkoff-Saxo) with Ian Stannard (Sky) a further second back.
Australia's Heinrich Haussler (IAM) is eighth overall, 44 seconds behind Terpstra.
The race returns to the open road with the fourth stage a 165.5km ride between Al Thakhira to Mesaieed.




(Niki Terpstra leads the 2015 Tour of Qatar - Getty)
Stage 3: 10.9km, Lusail Circuit - Lusail Circuit
1 Niki Terpstra (NED) Etixx-QuickStep 14min 04sec
2 Fabian Cancellara (SUI) Trek Factory Racing 0:00:08
3 Bradley Wiggins (GBR) Sky 0:00:09
4 Maciej Bodnar (POL) Tinkoff-Saxo
5 Ian Stannard (GBR) Sky 0:00:10
6 Matthias Brandle (AUT) IAM 0:00:18
7 Guillaume Van Keirsbulck (BEL) Etixx-QuickStep 0:00:20
8 Edvald Boasson Hagen (NOR) MTN-Qhubeka 0:00:21
9 Greg Van Avermaet (BEL) BMC 0:00:24
10 Reto Hollenstein (SUI) IAM 0:00:25
General classification
1 Niki Terpstra (NED) Etixx-QuickStep 7hr 53min 42sec
2 Maciej Bodnar (POL) Tinkoff-Saxo 0:00:11
3 Ian Stannard (GBR) Sky 0:00:12
4 Greg Van Avermaet (BEL) BMC 0:00:19
5 Luke Rowe (GBR) Sky 0:00:33
6 Alexander Kristoff (NOR) Katusha 0:00:36
7 Tom Boonen (BEL) Etixx-QuickStep 0:00:42
8 Heinrich Haussler (AUS) IAM 0:00:44
9 Andriy Grivko (UkR) Astana 0:00:46
10 Peter Sagan (SVK) Tinkoff-Saxo 0:00:48
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