Boasson Hagen was able to beat his two final breakaway companions, Terpstra and Oliver Naesen (IAM Cycling), to the line in Geraardsbergen.
Terpstra claimed the overall honours after Rohan Dennis (BMC) crashed and lost a significant amount of time.
The final stage was always poised to be the toughest of this year’s race as the 197km stage included 16 of the typical short steep Belgian Hellingen climbs, resembling a shorter edition of the Tour of Flanders.
The start was fast as numerous riders tried to get ahead in an early breakaway.
It took over 70km before a group of nine riders got clear.
The leaders were able to get a maximum gap of 2’45” before the multiple ascents of the Bosberg and Kapelmuur began.
The peloton began picking up the pace when the tough finishing circuit was reached. At the same time rain started to fall which made the cobbled climbs tricky and the roundabouts slippery.
When the riders hit the Bosberg at 46km to go, the race exploded and Boasson Hagen was perfectly placed to play his part at the front.
A big attack of six riders went over the top as the early break had faltered.
Boasson Hagen wasn’t part of that initial split but almost immediately he jumped across with two others to form a lead group of nine.
Overall favourites Peter Sagan (Tinkoff) and Dennis missed the split and so Terpstra had the most to gain as he and team-mate Bob Jungels drove the pace at the front.
For a long time, the gap hovered around the 15″ mark before the treacherous conditions eliminated a number of riders, among them Andre Greipel, Boy van Poppel and Dennis.
Between the falls and the tough ascents of the Bosberg and Kapelmuur, the race became one of sheer attrition and not many were left in contention.
From the original nine-man group up front, only three survived to take on the last 10km.
Boasson Hagen, Terpstra and Naesen pushed on to the finish in Geraardsbergen, with the Sagan chase group some 48″ behind.
On the final 1km climb to the line, Boasson Hagen showed he had enough left in the tank to take a fine victory ahead of Terpstra and Naesen.