The bonus point victory fulfilled the home side's part of the bargain though they were still reliant on London Welsh defeating London Scottish if they were to progress. Midway through the second half, that looked unlikely but a superb fightback from Welsh meant Pontypridd topped Pool 2.
Qualification completes a remarkable result for Pontypridd, given the nature of their fully professional pool opponents. They can now look ahead to the last eight and the way they played against the Academicals, despite the conditions, will give them hope of going all the way.
Geraint Walsh and Smith's first effort had put the home side 17-0 up at the break and they ran riot after the interval to sew up victory. Aled Summerhill and Owen Williams added further scores with a penalty try and Smith's second rubber-stamping success. Captain Simon Humberstone kicked five conversions and a penalty as the visitors failed to trouble the scorers.
At the final whistle, there was some waiting to be done but when the result from the Scottish game filtered through, the Pontypridd faithful went wild to celebrate qualification.
On a Sardis Road pitch left saturated by the recent rain, the home side started well as they defied the conditions to retain the ball impressively. Thomas Young knocked on with the line gaping but a sixth minute penalty from skipper Humberstone gave Pontypridd a solid start.
Needing a four-try bonus point to stay in the hunt of qualification for the quarter finals, Pontypridd were certainly determined to play but unsurprisingly, the nature of the pitch didn't help the spectacle. There were plenty of mistakes from both teams though the home side were enjoying some luck with kicks over the Edinburgh blitz defence.
When the first try arrived, it came from a clever chip ahead from Humberstone. Williams collected and although he was caught short of the line, Walsh's superb support line saw him dive over under the posts. Humberstone converted for a 10-0 lead.
The first quarter had seen the Academicals offer little in way of attack, fly half Alex Blair, brother of Scottish scrum half Mike, missing touch on a number of occasions. But when hooker Stuart McInally showed an impressive turn of foot to break clear, Pontypridd were indebted to an interception from Smith to keep their line intact.
As the rain came down, Pontypridd kept up the pressure, Humberstone putting a kickable penalty to touch in search of a second try. Their adventure was rewarded when Summerhill found Smith with a lovely inside ball. The young centre dived over and with Humberstone again adding the extra two, Pontypridd were halfway to a five point win at the break.
A monumental downpour as the players returned to the field failed to stop Pontypridd from taking firm control at the start of the second half. Another Humberstone kick caused carnage in the Edinburgh defence, Summerhill sliding through the mud to take advantage. The conversion went wide but with the game now in the bag, Pontypridd went in search of a fourth score.
Craig Locke came close to doing just that but dropped the ball as he looked for support and as the hour mark approached, both teams introduced replacements. New faces didn't exactly kick the game into life as the puddles on the pitch slowly turned to lakes.
The conditions must have put the game in doubt in the mind of referee Andrew Jackson but with the action continuing, Pontypridd shoved the Edinburgh scrum back to earn a penalty try. Humberstone converted and with London Welsh coming back at London Scottish, we were set for an exciting finish.
Things couldn't have worked out better for Pontypridd and further tries from Williams and Smith, the second a superb 90 metre dash, coupled with London Welsh's 18-21 defeat of London Scottish, meant the dream of British & Irish Cup glory lives on at Sardis Road.
Pontypridd: Tries: Walsh, Smith (2), Summerhill, Penalty, Williams Convs: Humberstone (5) Pens: Humberstone.