Melbourne won their third straight contest and announced themselves as the hottest team in the NBL heading into the final weeks of the regular season.
The duel between Ware and NBL leading scorer Jerome Randle (21 points) was worth the price of admission but, apart from the efforts of big man Daniel Johnson (14 points and 11 rebounds), Adelaide could not prevent United dominating throughout.
Melbourne exploded out of the blocks as Ware and Blanchfield combined for five three-pointers to build a 27-17 advantage in the first quarter.
Adelaide responded with six straight points to open the second term and stayed in touch until the hosts streaked away by amassing 24 points in the final five minutes to take a 60-43 halftime lead.
Goulding scored 12 points in United's pivotal second-quarter run, including another buzzer-beating triple, while Wesley displayed a series of low-post moves to keep the scoreboard ticking over.
United restricted Adelaide to just eight points in the third quarter to effectively end the contest.
Adelaide coach Joey Wright felt his side's lack of attention to detail was the most disappointing aspect of the loss.
"We didn't do most of the little things," said Wright.
"We didn't play with any passion. Our response to them making big plays or making any plays was pretty much neutral body language.
"We just weren't there tonight."
- AAP