With the Kiwi happy to sit two-thirds of the way down the field, he became slightly detached from the leaders through the 2km mark as world record-holder Lamecha Girma of Ethiopia stretched the field with a gradual injection of pace.
Showing great maturity, Beamish refused to panic and gradually started picking off athletes in front of him.
Eighth at the bell, he then launched his trademark kick and, in a late burst of speed, overhauled three athletes on the last lap to claim the highly-accomplished fifth-place finish.
His performance surpassed the previous best result by a New Zealand man in a track race at a world championships, by Nick Willis, who finished sixth in the 1500m final at the 2015 edition in Beijing.
Out front, the gold went to Morocco’s Olympic champion Soufiane El Bakkali, who secured a successful defence of his world title in 8m 03.53s. Girma won a third successive world steeplechase silver in 8m 05.44s, with Kenyan Abraham Kibiwot (8m 11.98s) rounding out the podium in bronze.