Essex 343 and 59 for 2 (Das 27*, Hume 2-14) trail Ireland 419 (Stirling 107, Tucker 97, McBrine 67, Richards 5-96) by 17 runs
Graham Hume then pushed his claims for a place in the XI at Lord's next week by removing both Essex openers in the same over.
Stirling, who scored his first Test hundred in Galle last month, had been expected to miss the game against England because of a deal to play in the Blast for Birmingham Bears, but was picked in the squad after a change of heart.
He only joined the tour match in Chelmsford on Saturday, having turned out for Birmingham in Leicester less than 24 hours previously, and was quickly making the adjustment to facing a red ball after walking out in the sixth over of the morning.
Ireland were 46 for 4 at that stage, and the score soon became 65 for 5 as Jamal Richards and Mark Adair - the Ireland seamer who is playing for Essex in this match - rattled the top order.
However, Stirling and Tucker set about repairing the damage with a stand that was eventually worth 175 in 30.1 overs.
Stirling brought up his half-century first, from 63 balls, with Tucker getting to the mark from 61 balls shortly after. Tucker, the wicketkeeper-batter, then accelerated towards a century with a flurry of boundaries, but required treatment for an arm problem on 96 and then cut tamely to backward point a few balls later.
With Stirling content to weigh anchor, Andy McBrine breezed to a 48-ball fifty against a tiring attack, as Ireland added 105 for the seventh wicket. Stirling brought up his century from 137 balls shortly before tea.
After the break, McBrine dragged on to his stumps to hand 18-year-old Noah Thaine a maiden first-class wicket, and Stirling miscued a pull off Richards with the second new ball. Fionn Hand's belligerent 48 not out from No. 9 extended Ireland's lead before Richards capped an impressive showing by completing a five-for on debut.
There was time for Essex to begin their second innings, and Hume struck twice in the space of five balls - Nick Browne caught behind and Josh Rymell taken at slip - but first-innings centurion Robin Das once again played his shots to be 27 not out from 26 at the close.