Harinath scored an undefeated 114 and Sangakkara made 83 as the pair shared a second-wicket stand of 142 to help propel the visitors to 297 for five by stumps, an overall lead of 76 runs.
Jake Ball was the most impressive bowler on display, returning figures of 3-77.
A wet outfield wiped out the entire morning session, leaving players and spectators alike having to come to terms with the news surrounding James Taylor’s enforced retirement from the game.
When play commenced at 2pm Ball was immediately clipped through midwicket for a brace of boundaries before adjusting his line slightly to trap Rory Burns lbw for 17.
Aided by some fluent cover drives and purposeful running, Sangakkara reached his fifty from 62 deliveries, with nine fours and was unbeaten on 83 at tea.
Church whipped the camera out and here is the moment Arun Harinath went to his century https://t.co/lWeo6RqQvb
— Surrey Cricket (@surreycricket) April 12, 2016
At that stage Surrey had reduced their deficit to only 58 and had two batsmen well set at the crease but the resumption tilted the balance back towards Notts.
Ball struck with his opening delivery of the final session, having Sangakkara caught behind by Chris Read, before following up with an identical dismissal to get Steven Davies for nought.
Jason Roy, who had blazed a punchy 28 in the first innings, helped Harinath wipe out the deficit with some powerful drives but the overall lead was only 12 when he was pinned in his crease by Brett Hutton for 37.
Harinath moved to 96 with his first maximum, hooking Hutton over the square-leg fence and then reaching three figures by sweeping Samit Patel fine for his 14th boundary, from his 182nd delivery.
Ben Foakes played his second attractive knock of the match but, as in the first innings when he fell for 38, he threw away the chance of a sizeable score when he chipped straight back to Patel for 26 after a stand of 55.
Surrey’s hopes of emerging unscathed – or better – will depend on Harinath being able to extend his innings deep into the final day, with the second new ball only seven overs away.
Notts seamer Harry Gurney said: “The pitch was probably a but little slower today but they batted very well. It takes it into an interesting fourth day and it’s a cricketing cliché, the first hour will be very important.
“The second new ball will be crucial, hopefully we can knock them over quickly and not have too many to chase.”