Sibley, on 169 overnight, eventually added 334 in 53 overs with Lawrence, a fourth wicket record for Surrey against Durham.
Lawrence cruised from 58 at the start of the day to 178 – his first-class career best – before slicing Daniel Hogg to point.
Lawrence struck four sixes and 19 fours in an eye-catching 149-ball effort, while Jacks was just as effortlessly brutal in his own 119 from 94 balls – also hitting four sixes. Sibley and Jacks put on a further 133 in 21 overs for the fifth wicket.
The declaration came when Jacks skied Hogg to deep mid-off looking to hit a third successive six, after Surrey had opted to bat on after tea for what proved to be another 12 balls and 17 runs.
But the first post-tea Jacks blow off Hogg, swung high and far over a short mid-wicket boundary, took Surrey past their previous highest total in first-class matches – the 811 scored against Somerset at the Oval in May 1899.
Sibley’s 475-ball epic, featuring two sixes and 29 fours but for the main part, a relentless display of risk-free accumulation, was the eighth first-class individual score of 300 or more by a Surrey batsman, and the seventh highest.
The former England Test opener joins an illustrious list topped by Bobby Abel’s 357 and also includes Kevin Pietersen, Walter Read, Sir Jack Hobbs, Tom Hayward, Andy Ducat and Mark Ramprakash.