Australia declared nine down for the second time in the match, leaving the tourists chasing either a world record fourth innings target of 468 or attempting to bat out more than four sessions to cling to a draw.
Neither outcome looked particularly believable as Hameed gloved a fine ball from Jhye Richardson in the second over, continuing a grimly predictable sequence for the openers. Hameed and Rory Burns have now shared opening stands of nought, 23, seven and four, routinely handing the hosts a new-ball sacrifice.
Burns and Dawid Malan reached the interval on 20 for one, with a challenging period under floodlights next up on the menu.
Australia had earlier finished up on 230 for nine, with half-centuries for Marnus Labuschagne and Travis Head and four wickets split between the part-time spin of Joe Root and Malan.
England cut an increasingly passive sight as they meandered in the field, at one stage even asking Sussex seamer Ollie Robinson to turn in three overs of gentle off-breaks.
The day began with England already behind by 282 and, temporarily at least, captainless. Things had taken a darkly comic turn when skipper Joe Root was hit in the groin while taking throwdowns from spin coach Jeetan Patel in the warm-ups and a precautionary trip to hospital left Ben Stokes leading the team out.
Despite the overbearing match situation, England went on to enjoy possibly their most incisive passage of bowling to date. They kicked off the opening session by taking three for 10 and it might have been even better had Jos Buttler’s rollercoaster match with the gloves not continued.
James Anderson made short work of nightwatch Michael Neser, ripping one between bat and pad and taking out middle stump, before Stuart Broad outclassed the off-form Marcus Harris.
Buttler took a brilliant diving catch after a late edge whistled towards first slip, surely hoping to have put his two costly drops in the first innings behind him. Those hopes were crushed almost instantly, as he dropped Australia captain Steve Smith off the very next ball.
Broad gave him a perfect welcomer, snaring the edge and beginning to throw his arms out in celebration only for Buttler to go one-handed again and parry the chance. Broad shelved his disappointment to follow up with another fine delivery, thumping Smith’s front pad in front of off stump and racing off in celebration. Umpire Rod Tucker was unmoved and the DRS technology just allowed his call to stand.
Mercifully, Smith was unable to make his good fortune stick as he fell for six, brushing Robinson off his hip to leave Buttler another tricky chance.
In keeping with his unpredictable, up-and-down match, he held on. Soon after Stokes invited Robinson to experiment mid-spell with off-spin and the sight of the 6ft 6in seamer rolling his way through three overs of inoffensive twirlers took what has been a dispiriting match into new and faintly bizarre territory.
From there, the game drifted towards the decisive moment when England would be called to bat again. Marnus Labuschagne and Travis Head shared a stand of 89 to keep their side in control of the narrative, both striking 51 before being dismissed.
Robinson got Head after going back to the day job with another spell of pace but four of the last five wickets were shared by two more occasional spinners. Root returned to the field and took care of Alex Carey and Mitchell Starc, while Dawid Malan’s lesser-spotted leg-breaks also got an airing.
He opened his Test account when Stokes pulled off a brilliant catch deep on the midwicket boundary to see off Labuschagne and closed the innings when Jhye Richardson sprayed a top edge to Buttler.
That left eight overs for England to bat but two was enough for Australia to get on the board, Richardson probing Hameed with a tempter that lifted sharply and had him caught behind off the back glove.