Surrey lost three of them as they slipped from 366-7 overnight to 414 all-out, Ollie Pope finishing on a career-best, unbeaten 158.
Yorkshire also lost three wickets in reaching 40 in reply, openers Alex Lees and Adam Lyth departing inside the first four overs and overseas player Cheteshwar Pujara suffering his sixth failure in seven innings.
When the rain started falling 10 minutes before lunch, after which there was no further play before proceedings were abandoned at 4.30pm, Joe Root was unbeaten on 14 and Harry Brook undefeated on one.
It spelled frustration for the Surrey bowlers, who had been on the charge beneath the overcast skies only to be denied the opportunity to make further inroads.
Pope had 131 to his name when the day began, his third hundred in only his 10th first-class match.
The 20-year-old had showed wristy improvisation on the first day, helping Surrey recover from 69-4 after acting captain Root had sent them into bat, and he picked up from where he left off with a deft cut for four off Steve Patterson.
Yorkshire landed an early blow, however, when Tim Bresnan had Conor McKerr caught at first slip by Pujara, who grabbed the rebound when Lyth failed to take the initial chance at second slip.
McKerr added only two to his overnight 27, and his dismissal ended a partnership of 82 with Pope in 14 overs.
Jade Dernbach arrived and appeared in little mood to support Pope through watchful defence, throwing the kitchen sink at a delivery from Bresnan that he carved over backward-point for six to bring up the 400, much to the bowler’s bemusement.
After Pope went to 150 from 216 balls, Dernbach’s cameo ended not unpredictably when he slogged Patterson to Root at mid-off.
The innings ended when Amar Virdi steered Bresnan to third slip, where Jack Leaning pulled off an athletic catch, leaping to his right.
Bresnan finished with 3-98 and Patterson 3-107, Pope’s 158 spanning 224 balls and including 27 fours.
Recalled to the team after captain Gary Ballance pulled out with a bug, Lees fell for a golden duck to the second ball of the reply, edging Dernbach to Dean Elgar at third slip.
The total became 7-2 when Lyth was trapped lbw trying to drive Sam Curran, who was so confident of winning the decision that he celebrated before the umpire’s finger was raised.
Pujara uppercut Dernbach for six to get off the mark but did not linger, caught low down at second slip by Scott Borthwick off Curran to leave Yorkshire 34-3.
Root square-drove Dernbach for a handsome boundary, but the south London skies soon filled in.
“We are three down and need a couple people to stand up and make scores,” said Jonny Bairstow ahead of day three.
“It’s done a bit with each new ball, making those periods important. It flattened out for them when the ball got older, and hopefully it’s the same for us.
“The pitch has been under covers since lunch. They’re covered sheets not aired sheets, so I’m sure there will be some moisture in it tomorrow. We need to get through that first period and go from there.”