Pope's 205, the fastest double hundred in a Test in England, and Duckett's 182, the quickest 150 in a Test at Lord's - were the cornerstones of a huge first innings total of 524-4 declared.
That left England 352 runs ahead on first innings.
Ireland then slumped to 18-2 before reaching 97-3 at stumps, with fast bowler Tongue, who struck twice in an over, taking all the wickets in a return of 3-27 in eight overs.
Harry Tector (33 not out) and Lorcan Tucker (21 not out) held firm on a good pitch but Ireland were still 255 runs away from avoiding an innings defeat.
Worcestershire quick Tongue had gone wicketless on Thursday.
But in another selection coup for coach Brendon McCullum and skipper Ben Stokes, he struck with his first ball Friday when Peter Moore was plumb lbw for 11.
Five balls later, Ireland captain Andrew Balbirnie - who had avoided the embarrassment of a 'pair' at the Home of Cricket - was caught behind carelessly chasing a wide ball from Tongue.
Ireland now risked being beaten inside two days in a match scheduled for four rather than the usual Test maximum of five.
James McCollum, who had top-scored for Ireland with 36 on Thursday, then retired hurt on 12 after twisting his right ankle trying to pull a Tongue short ball.
Tongue then had Paul Stirling out gloving down the legside to wicketkeeper Jonny Bairstow.
Earlier, Duckett and Pope ran riot against an outclassed attack lacking the experience of the Ireland bowling unit that reduced England to 85 all out in a corresponding Lord's clash four years ago.
Both batsmen scored a hundred runs in a session on Friday, left-hander Duckett achieving the feat in the morning's play and Pope in the afternoon.
And Duckett, by making a run-a-ball 150, surpassed Australia great Don Bradman's record of 166 balls for the fastest Test 150 at Lord's, in what was also the England opener's first Test on home soil.
Ireland, in just their seventh Test and still searching for a first win at this level, had few answers to the run-spree, with seamers Mark Adair and debutant Fionn Hand both conceding over 100 runs each.
Joe Root helped himself to 55 as he became just the 11th batsman, and second Englishman after Alastair Cook, to score 11,000 Test runs before giving his wicket away.
Pope, went on to a maiden Test double century after tea in style by driving off-spinner Andy McBrine six to reach the landmark in just 207 balls faced.
But the next delivery saw a charging Pope stumped comfortably, with Stokes then declaring.
England had resumed just 20 runs behind after veteran seamer Stuart Broad had taken 5-51 in Ireland's first innings 172 on Thursday.
Duckett was 60 not out, with England vice-captain Pope unbeaten on 29.
A morning and wicketless run spree took England to 325-1 at lunch.
But a replacement ball did the trick for Ireland, with Duckett playing onto medium-pacer Graham Hume having faced just 178 balls, including 24 fours and a six.
The first Ashes Test at Edgbaston starts on June 16th but before then Australia face India in next week's World Test Championship final at the Oval.
