Cook got no further than the fourth over of the morning, and added just three runs to his overnight 14, before an indeterminate prod forward resulted only in an edge low to slip off Dhammika Prasad.
Ballance announced himself with a cut for four off the same bowler to get off the mark, but neither he nor Robson proved to be in any rush.
Instead, they established themselves at a traditional Test match tempo - and the relative slow grind served England's purpose ideally.
Robson passed his maiden 50 before lunch, from 102 balls, and Ballance had faced 14 more when he reached the landmark in mid-afternoon with another cut for his seventh four - off Nuwan Pradeep.
If memorable highlights were thin on the ground, there were relatively few alarms either from a second-wicket pair as yet sharing just five caps between them.
Ballance was reprieved by DRS on 31, when Rangana Herath - and umpire Billy Bowden - thought he was lbw, only for simulation to depict the slow left-armer turning the ball more than the width of the stumps.
Robson might have gone lbw too on 78, to Prasad, had the bowler appealed when his yorker hit the batsman on pad before bat.
In between, on 61 Ballance offered a sharp chance off Herath straight to short-leg - where Kaushal Silva could not hold on.
The partnership therefore remained intact until Sri Lanka captain Angelo Mathews, who finally brought himself on for the 66th over, struck with his ninth delivery.
Ballance was beginning to threaten a second successive century, in only his third Test, when the medium-pacer had him caught-behind pushing forward.
Robson took tea on 98 and turned that into an even hundred when forcing Prasad into the covers for two moments into the evening session.
