In reply, British Universities stuttered to 82 for 5, before Luke Parker and Josh Knappett steadied the ship, leaving the students on 190 for 5 at close, with a draw the most likely result on the third day.
Michael Yardy was the star of the match, notching up 35 fours and two sixes in a towering 257 – the highest score of the English first class season so far – which led Sussex to 549 for 7 declared.
The tourists' bowlers lured the county batsmen into playing odd strokes to loose balls, but not Bilal Shafayat, who made 76 before mistiming one off left-arm spinner Enamul Haque.
However, 16-year-old prodigy Mushfiqur Rahim continued his good run of form, scoring 115 not out with 15 fours and a six to lift the Bangladeshis to 309 for 7 in their glorified nets session.
The English mixed the odd good length ball with the short and wide stuff, inducing edges through to the slips at regular intervals – although, admittedly, the Bangladeshis would never have been out if they'd tried to play a bit more defensively.
An hour after tea, England brought up the lead, with Strauss having notched his fifty despite looking slightly shaky against Anwar Hossain Monir's bowling, and then being dropped on 51.
Four overs later, the patient Rafique finally got his reward, Khaled Mashud coming up with a magnificent catch to get Trescothick out six short of a double century.
Yet again, they failed to play the short ball well enough, and lost five wickets – Simon Jones and Andrew Flintoff the main culprits, taking two each – for a miserable 65 before Khalid Mashud and Aftab Ahmed took some responsibility and guided them to stumps with 95 for 5.
Only six balls into the third day, Hoggard bowled a good off-cutter to Aftab Ahmed, who failed to play it properly and was hit on the pads – out for a fine 32, Bangladesh's highest score in the Test series so far.
Simon Jones eventually broke through the defences, though, as Anwar Hossain Monir got a standard thick edge to first slip Trescothick, and thus the ninth wicket fell – 156 for 9.
Gareth Batty – England's spin-bowler, who came in to replace the injured Ashley Giles – was only mentioned on the official scorecard once, as he did not bat, did not bowl, and did not hold a catch.
A thoroughly professional bowling performance from the England bowlers followed, with Harmison, playing at his home ground, making the most of the conditions to take 5 wickets as the clearly outclassed Bangladeshis succumbed for 104.
(Cricinfo scorecard) After a poor first-class section of the tour, Bangladesh were hoping things would improve on the one-day leg, particularly after their spirited second innings in the Second Test.
In a disciplined bowling effort, Nazmul Hossain took two early wickets, Worcestershire collapsed to 168 (despite Bangladesh giving up 33 wides and 6 no-balls), and in a slow, gritty chase, the Bangladeshis – guided by Habibul Bashar's 26 not out and 43 from Javed Omar, made it to the target with 14 overs to spare.
(Cricinfo scorecard) Amid rains at The Oval, Jon Lewis had a stunning ODI debut for the English cricket team against Bangladesh, removing Javed Omar and Mohammad Ashraful with successive deliveries before taking out Nafees Iqbal in a good opening spell.
Marcus Trescothick hit his ninth One Day International century off just 76 balls, Andrew Strauss supplied with a level-headed 82, and ten extras added up to a total of 192.
(Cricinfo scorecard) Perhaps the biggest upset in the history of limited overs cricket, Mashrafe Mortaza shocked the Sophia Gardens crowd when he had Adam Gilchrist plumb on the second ball of the second ODI, taking the first Australian wicket without a run yet on the scoreboard – and it was to set the tone of the match.
Most people would have expected Australia to swamp Bangladesh, especially after the 10-wicket defeat the Bangladeshi Tigers endured in the opening match with England, but a maiden from Mortaza gave them some hope, at least.
Hogg and Clarke leaked runs like a drain, six wides were bowled, and Mohammad Ashraful showed another glimpse of why he's been called Bangladesh's finest batsman.
As he made the second ODI hundred in the Bangladesh team's history, he forged a massive 130-run partnership with Habibul Bashar, and had a great two hours at the crease (although dropped on 54) – before picking out Jason Gillespie at long on to be out for exactly 100.
Bangladesh still needed 23 runs off 17 balls, but Aftab Ahmed continued his fine form from the Oval match with England, as he first took a leg bye off Ashraful, then gave the strike to Rafique, who smashed a cover driven four before taking another legbye.
Thus, it became a formality – Bangladesh won with four balls and five wickets to spare, almost convincing in today's cricket, and the result meant that the Aussies needed a victory over England at Bristol the following day to have any chance of winning the group stage.
After a bit of a shaky start, with Andrew Strauss being dropped, but Marcus Trescothick smashed boundaries to all corners as Bangladesh's bowlers were made to look distinctly ordinary.
Chris Tremlett, England's ODI debutant, started well with good pace – near 140 km/h – while Jon Lewis served up full tosses and wides from the other end.
Overall, England could take some good batting form from their openers and a stunning debut from Tremlett – who looked much more impressive than Lewis in this game – out of the match, while Bangladesh could be happy with the swashbuckling Ashraful and Nazmul's three wickets.
Under leaden skies at Old Trafford, Ricky Ponting made the wise decision and chose to bowl, and short-balls from Brett Lee immediately had the Bangladeshis worried.
Tushar Imran was next to fall to Lee, and many expected a procession to begin, but Shahriar Nafees and Mohammad Ashraful gave the crowd a treat with some special strokes.
Habibul Bashar won the toss and batted first, and it looked to pay off as Shahriar Nafees, Javed Omar and Tushar Imran milked runs off the English opening bowlers.
However, their opener Javed – whose ODI strike rate was just above 50 at the time – slowed things down, and a double blow from Andrew Flintoff – first getting Tushar with an inside edge to have him bowled, and then Mohammad Ashraful for a golden duck – Bodyline-style.
With Aftab Ahmed falling for 15, it was up to wicketkeeper Khaled Mashud who did an excellent job in lifting Bangladesh past 200 – taking a particular liking to Gough as he made 42 not out off 43 balls.