Instead, after lurching at one stage to a perilous 47-5, England were rescued by a record unbroken stand of 244 – the best by anyone for the eighth wicket against Pakistan – between Trott (149 not out) and Broad (125no) in a stumps total of 346-7 on day two of the fourth Test.
Both passed 1,000 Test runs in the course of their innings, Broad on his way to a maiden first-class century and Trott little more than a year after his Ashes-clinching debut at The Oval.
Yet it was Aamer (6-73) who had made the first bid for the headlines when he became the youngest bowler ever to 50 Test wickets and only the second Pakistani to take six in an innings on the hallowed turf.
As England recovered from a rash of middle-order ducks at the hands of Aamer, in a match Pakistan must win to square the series 2-2, this was a day to intrigue the purists as well as delight the statisticians. At a venue where Trott made a double-hundred against Bangladesh earlier this summer, he responded with a 195-ball century in which he alone – until Broad moved into outright counter-attack – had the mastery of Aamer.
Trott used the crease and advanced out of his ground to try to negate Aamer's swing under initial heavy cloud cover in an innings which was to be peppered with his trademark, straight-bat clips to leg off the back foot. Broad, by contrast, stood tall to strike the ball on top of the bounce through the off side and down the ground in a partnership which more than trebled the total from 102-7.
England's prosperity – begun by Trott and Matt Prior in an important 50 stand for the sixth wicket – was unthinkable when 18-year-old Aamer was wreaking havoc in the first 20 minutes of the day.
Belying his age to make such telling use of conditions and tame the Lord's slope like an old hand, the left-armer took four wickets for no runs in eight balls.
After Trott and Prior had apparently drawn his sting, Aamer then returned to take two wickets in an over immediately after lunch – only for Broad to help England's No 3 take over.
After becoming only the third Englishman to reach three figures from No 9, Broad said: "It was amazing.
"It's a feeling I'll remember for the rest of my life.It is one of those days that will live long in my memory.
"I had a bit of licence (to attack (when I came in). But I also knew that if we were 110 all out this Test series was going to be
"So I looked to take a bit of responsibility to bat with Trotty, because I know he can bat for long periods of time and score big hundreds.
"I wanted to be aggressive and take the attack to the bowlers, but I had to do it in a manner that I didn't give my wicket away cheaply."
Kevin Pietersen continued his worrying run of form with a golden duck – his the first of successive noughts from batsmen four, five and six.
Pietersen was the odd man out in that he contributed much to his own downfall, rather than being prised out by a delivery of the highest class.
He simply drove at a wide, swinging ball from Aamer and got an obliging edge behind – safely collected by Kamran Akmal.
The Pakistan wicketkeeper, one of several less than reliable catchers in the tourists' ranks this summer, had already done the decent thing from the final ball of the previous over when Aamer got one to go down the slope from the pavilion end to have Alastair Cook also caught behind.
Paul Collingwood survived the hat-trick ball but got little further before a review of Billy Bowden's not-out lbw decision proved Aamer had swung the ball past the bat and in line.
Eoin Morgan pushed defensively at more swing from Aamer to edge to second slip and fall – like Collingwood – to the third ball he faced.
Then Prior was mightily close to making it four ducks but stood his ground when Umar Amin's low catch from a speared drive at Aamer in the gully could not be proven to be clean by inconclusive footage.
Trott and Prior showed survival at least could be achieved with skilful batting – and an equal share of reasonable fortune – until the latter followed one that held its line from Aamer to have him caught behind.
Graeme Swann took just two balls to make it four ducks for England after all – driving Aamer, as Prior had two-and-a-half hours earlier, low to gully where there were no doubts this time about Azhar Ali's catch.
Trott was past his 1,000 Test runs by then, but it will clearly take many more to satisfy him.
He was certainly not about to squander this opportunity, he and Broad gradually softening up an attack which had seemed sure to make short work of their hosts yet ended up conspicuously unable to land the killer blows. As skies brightened, Lord's predictably flattened.
When Aamer switched to the nursery end just before tea, he was dispatched by Broad for six over the heads of two boundary fielders on the hook.
By the time the second new ball was available deep into the evening session, Broad was well on the way to a hundred which would feature that six and nine fours from 159 balls and put him in an elite club of cricketers whose first three-figure score has come at the highest level.