Draper, 22, needed to come by way of a critical examination however displayed nice endurance as he outlasted the higher-ranked Kecmanovic to arrange a quarter-final towards American high seed Tommy Paul.
After Draper conceded a good first set when he misplaced serve within the twelfth recreation, the second continued right into a tie-break wherein the Fifty fifth-ranked Serb rallied from 5-2 down to achieve match level.
However, on the point of defeat when trailing 8-7 after which 9-8, world quantity 62 Draper clinched his fourth set level to pressure a decider.
One other restoration was required as that too went the space, with Draper heading for defeat at 4-1 down within the concluding tie-break.
The Briton gained 5 of the subsequent six factors to achieve match level for the primary time and he closed out an epic contest on the third alternative to win a 5-7 7-6 (11-9) 7-6 (9-7) after three hours and 39 minutes.
Nonetheless, British quantity two Evans was unable to hitch Draper within the final eight after dropping 4-6 6-2 6-1 to Kazakh eighth seed Bublik.
Making his return from harm in Adelaide following the calf tear he sustained in Vienna in October, Evans, who impressed in his opening win on Tuesday, made a promising begin to take the primary set towards the world quantity 31.
However the match unravelled quickly for the Fortieth-ranked Evans after he fell a break of serve down within the second set, with Bublik cruising to victory by profitable 10 of the final 11 video games.