Wales led 14-7 against New Zealand, who had already claimed the overall series honours earlier in the tournament, in a thrilling semi-final encounter.
Tries by elusive Lee Williams and Adam Thomas, both converted by Alex Walker put Wales in the driving seat at the break.
But the Kiwis showed their class in the second spell and fought back to race over for three tries through Gillies Kaka, Tomasi Cama and Lote Raikabula to waltz into the final with a 26-14 victory.
Wales had to quicky put that disappointment behind them and face England in the play-off for third.
But once again, despite getting off to a great start, Wales suffered a heartbreaking 24-21 defeat after the final hooter had gone, surrending a 21-7 halftime lead.
Llandovery's Chris Knight, making his tournament debut for Wales, replied to an early touchdown by James Rodwell to level the score after five minutes.
Wales snatched control of the game thanks to tries by Alex Walker and Rhys Shellard and with Walker adding the extras, victory was within their grasp.
But England hit back in the second half through Rodwell and the electric pace of Dan Norton to set up a tense finale.
Dogged defence kept the red rose brigade at bay but with just over a minute remaining Sam Edgerley blitzed the dogged Welsh resistance to cross for the match-winning try. Christrian Lewis-Pratt's conversion just added salt to the wounds.
Wales head coach Paul John will take comfort from the fact that he's successfully integrated a new batch a players into the squad and all performed admirably.
Playmaker Gareth Davies impressed on his return to Sevens - so much so he finished the tournament as the fourth highest points scorer (with 32) and was selected in the Glasgow Sevens Dream Team.
Knight didn't look out of place in his debut tourament while Owen Williams showed his try-scoring prowess hasn't abandoned him while he's been on Cardiff Blues duty.
Wales will now head to next week's final round of the series in London where Kenya, Canada and New Zealand await in their pool. On today's evidence, they have nothing to fear, even against the mighty All Blacks.