Pohjanpalo opened the scoring in the 16th minute with a clever backheel inside the six-yard box.
Leonardo Benedetti levelled for the visitors on the half hour mark when he side-footed home a square pass from Gerard Yepes.
Pohjanpalo had his brace in the 36th when he converted a penalty awarded for a clumsy challenge on Dennis Johnsen.
The Finnish international had his hattrick in the 58th with an acrobatic diving header that left Sampdoria keeper Filip Stankovic with little chance.
Manuel De Luca made it 3-2 in the 65th minute with a first-time chip over the keeper after being played in on goal.
Fabio Depaoli equalised for Sampdoria just six minutes later with a header that should have been easily claimed by Jesse Joronen.
Gianluca Busio put Venezia ahead again in the 74th after getting a foot to his own header attempt that was initially blocked by the defender.
Mikael Ellertsson sealed the deal for Venezia in the 77th with a half volley that left Stankovic rooted to the spot.
Venezia are second, four points behind leaders Parma. Sampdoria are three points above the relegation playoff zone.
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