Trott (211no) batted almost 11 hours, hitting 17 fours from 403 balls, as his team established a first-innings lead before eventually declaring on 624 -8 in reply to 504-8 in late morning on the fourth and final day.
A fourth career double-hundred was a personal triumph for the painstaking Trott, South Africa-born and back on the ground where he made his first-class debut as a teenager 15 years ago.
His efforts helped the Lions out of a spot of bother, too, from 67-3 at one stage, as he and a succession of partners piled on the runs.
James Vince played an important part with the first of five half-centuries from No 5 downwards, to complement Trott’s immovability at No 4.
The captain was able to resume on 176 out of a day-three stumps total of 507 -6 alongside Yorkshire’s Liam Plunkett.
The fast bowler duly became the third of four Yorkshire players to pass 50, reaching his milestone before mishooking Chris Morris to long-leg to end a stand of 106.
Young Durham seam bowler Mark Wood made only five, before Trott was joined by Yorkshire’s Jack Brooks who hit a career-best 53 not out – just his second first-class 50 – from 37 balls and containing five fours and two sixes.
Trott then called time to see if his bowlers could make any inroads in just over two sessions remaining.
On a stubbornly docile surface, they could not.
First-innings centurion Gihahn Cloete was undone by marginal low bounce to go lbw to Boyd Rankin, and fellow opener Stiaan van Zyl was caught behind by Yorkshire’s Jonny Bairstow off the leg-spin of his county team-mate Adil Rashid.
But after the hosts reached 92-2 at tea, Trott and opposite number Rory Kleinveldt agreed a draw.
The second and final unofficial Test will get under way in Bloemfontein on Sunday.