Batty showed all his experience during spells from both ends to claim figures of four for 73 and make the visitors battle hard for their slender 42-run lead.
At the mid-point of the match Durham, who have yet to win a championship match in SE11 since becoming a first-class county in 1992, had reached 279 for nine in response to Surrey's dramatic first innings of 237.
Dale Benkenstein's unbeaten 70 was chiefly responsible for Durham's advantage after he and Batty sparred for much of a post-tea session that ended with honours just about even.
Warwickshire and Middlesex settled for a battle for bonus points in their rain-affected match at Edgbaston.
The match was effectively over as a contest once Warwickshire saved the follow on by reaching 279 when Tom Milnes clipped England paceman Steven Finn for a legside four during the 12 minutes of play that were possible before lunch.
The weather improved after the interval which allowed Tim Murtagh to complete his second five-wicket haul of the season and help Middlesex secure a second bowling point.
Rikki Clarke's aggressive unbeaten 66, meanwhile, helped Warwickshire to reach 374 for eight and collect two more batting points.
Although Middlesex took 10 points from a rain-ruined game, Warwickshire will be satisfied with their eight-point haul having been on the back foot for most of the match with an injury-depleted attack.
Leicestershire followed the logical course by batting through much of the final day against Division Two rivals Worcestershire at New Road.
Having lost three wickets in picking up two more bonus points before lunch, they kept Worcestershire in the field until tea-time, with Shiv Thakor making an unbeaten 52 prior to a declaration at 379 for eight.
In the 20 overs before the captains shook hands at 4.50pm, the home side made 61 for one, nudging into a lead of two runs after Jigar Naik had dismissed Matt Pardoe for his sixth wicket in the game.
The game between Gloucestershire and Hampshire also finished in a draw at Bristol.
Australian Michael Klinger's 163 helped Gloucestershire achieve maximum batting points before declaring their first innings on 400 for four, a lead of 126, shortly after lunch.
Alex Gidman made 69 but brother Will aggravated an ankle injury when sending down only the second ball of Hampshire's second innings and the visitors survived comfortably enough, closing on 120 for four, Michael Roberts making 44.
Gloucestershire took 11 points from an impressive all-round display, while Hampshire collected six from a below-par effort.