The 23-year-old was fourth at the turn with 50m of the race remaining.
However, he kicked hard during the final lengths and proceeded to go past the Japanese duo Ryo Tateishi and Kosuke Kitajima, recording a time of 2:07.43 in the process - a British record.
His effort was not quite enough to take the gold from Daniel Gyurta though, with the Hungarian posting a world record time of 2:07.28.
There wasn't such good news for Jamieson's compatriot Andrew Willis. The Brit appeared to be keeping pace with Jamieson with around 40m remaining, before eventually slipping down the field and finishing the race last.