Surrey, three times County champions in the past four years, were restricted to 328 in their first innings before Warwickshire replied with 544.
Dan Mousley made 144, and put on 212 for the third wicket with Sam Hain (94), giving the Bears a first innings lead of 216.
Surrey then hung on to secure the draw courtesy of a record partnership of 217 between Jamie Smith and Dan Lawrence to bat through the final day and finish 447-4.
Barnard, leading the side in all formats this summer for the first time, admitted he has now got real competition for places.
“We had some selection headaches going into the first game. Leaving some of the lads out was a tough decision,” he said.
“There were plenty of players putting their hands up and deserved to play, but it’s really pleasing to see the lads that got the nod coming through and showing their colours and played really good cricket.
“It’s great we’ve got the squad now which means we can move forward and take into account conditions and how people are feeling, and we won’t have to play the same team every week.
“It’s a really positive thing to have that depth. Yes, it throws up some selection dilemmas, but that’s what we want”.
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