The delivery was slanted across the left-hander on a perfect length, and Stoneman, pushing forward, edged it to wicketkeeper Jonny Tattersall, who took the catch as he tumbled to his left.
Thompson peeled away in celebration of his maiden first-class wicket, soon to be joined by his Yorkshire team-mates.
And although Stoneman might not be quite the scalp that he was when he played 11 Tests for England, the last of them more than a year ago, he was still a notable one for the Leeds-born all-rounder, handed his debut in the absence of David Willey, who is not playing due to family reasons.
Thompson added the scalp of Scott Borthwick – who played one Test for England in 2014 – on his way to 2-41 from 19 overs.
It was a respectable return on a respectable day for the visitors, who stuck at it as Surrey scored 290-8 as the match finally got going on day two.
At 265-4, Surrey were in the ascendancy before Yorkshire captain Steve Patterson struck three times in an over with the second new ball, Patterson taking it himself because Duanne Olivier was off the field with a groin injury.
When play ended at 6.05 amid biting winds and flapping marquee tents, the conditions more reminiscent of January than June, Patterson had figures of 4-71 from 24 overs.
Thompson, whom coach Andrew Gale believes also has the talent to score first-class hundreds, said: “We’ve come out on top there, that’s how we feel.
“Hopefully we can finish them off quickly in the morning and then get batting.
“It was great to make my debut, and I just told myself that it’s a game of cricket and that you’re doing what you’re doing every week.
“It was a matter of sticking to what I’ve done well in the twos in the past few years.”
The first and most remarkable aspect of yesterday’s play was that there was any play, given the volume of rain that washed out the opening day.
Many county headquarters would have struggled to get the ground ready for an 11am start, let alone a club venue such as this, but although Guildford falls short in comparison to its larger brethren in terms of facilities, its drainage system is well regarded.
With the outlying areas still damp and the skies overcast on a breezy morning, it seemed an obvious decision for Yorkshire to exercise their right to bowl as the visiting side. There was a bit there early on, perhaps, but the pitch was slow and sluggish and did not encourage particularly dynamic cricket with bat or ball, although a flurry of early boundaries by Stoneman off Ben Coad emphasised that batsmen still got value for their shots.
In front of around 1,000 spectators, Yorkshire kept plugging away against talented opponents.
Stoneman showed the class that won him his Test caps in the first place, driving fours on both sides of the wicket, while opening partner Dean Elgar gave watchful support.
Elgar, celebrating his 32nd birthday, was promoted up the order in the absence of Rory Burns, the Surrey captain withdrawing from his first Championship match for four years due to a back injury.
In the end, it took a loose shot from Elgar to bring the first wicket, the South African left-hander reaching for a wide ball outside his off stump from Patterson, which he steered to Dom Bess, fielding at point.
Stoneman went to fifty from 66 balls with 10 boundaries but was second out when Thompson induced the edge to Tattersall, which left Surrey 98-2 just before lunch.
It was the first delivery of Thompson’s fifth over from the Railway end, Stoneman departing for 61 from 72 balls.
After the break, Yorkshire put the squeeze on the scoring, with Coad particularly impressive in a second spell of 1-11 from seven overs.
Coad it was who took the third wicket at 142 when Ryan Patel was plumb lbw trying to turn to square-leg, the left-hander having survived a loud lbw shout from the previous delivery.
When Thompson had Borthwick flashing to second slip, where Adam Lyth took a chest-high catch, Surrey were 147-4 and beginning to falter.
But acting captain Ben Foakes and Championship debutant Jamie Smith, 18, wrested back the initiative, taking their team to 212-4 at tea and then to 265 before Patterson’s triple-wicket over wrested it back to Yorkshire once more.
First, Foakes was bowled for 62 from 115 deliveries from the first ball of Patterson’s 21st over, then Will Jacks shouldered arms to the second and Smith was bowled driving at the sixth to depart for 56 from 117 deliveries.
Coad followed up by having Rikki Clarke lbw before bad light ended play with nine overs of a possible 104 left.
Stoneman said: “Hopefully we can build on today and make some inroads with the ball. It would be nice to get another batting point tomorrow and then we’ll let our seamers run in and do their thing.”