The left-hander made 114 not out after the start of play was delayed until 14:00 BST because of a wet outfield.
He shared a stand of 142 with Kumar Sangakkara, who was caught behind off Jake Ball for 83 soon after tea.
Pace bowler Ball claimed 3-77, but Surrey, having followed on, reached the close on 297-5, a lead of 76.
Harinath scored 568 runs in eight first-class appearances for Surrey last summer, including two centuries.
He again showed a clam temperament to hold the innings together with one six and 15 fours after Rory Burns (17) was lbw to Ball in only the second over of the day.
Sangakkara also looked in good touch before he and Steven Davies departed in similar fashion in the same Ball over.
Jason Roy made a typically assertive 37, but was then lbw to Brett Hutton, leaving Harinath to bring up his century with a sweep for three off Samit Patel.

The advert from the Northamptonshire Police & Crime Commissioner (PCC) called for someone who was "resolutely client-centred and victim-focused".
The campaign group said PCCs were "serial offenders" in using "jargon".
Adam Simmonds, PCC, said: "The best communicators talk to people using the type of language they understand."
The existing chief constable, Adrian Lee, will be leaving the force in July.
The candidate information pack said the force was looking for an "agent of change" who can get "client-side" and "is a pioneer in blue-light collaboration".
Steve Jenner, spokesman for the Plain English Campaign, said: "The sentence that 'our chief constable must be able to see beyond the horizons of convention to make the paradigm shift' is a prime example of 'ploddledegook'.
"Police and crime commissioners seem to be repeat offenders in this regard for their mangling of the English language and this advert is borderline criminal.
"Senior police officers are probably used to this kind of jargon so they will understand it but the danger is they use it when they talk to the public."
The information pack also said the chief constable should not just issue "management speak from above" because "inevitably such statements of corporate aspiration can feel like yet another list of jargon and management-speak".
In response to the criticism, Mr Simmonds said: "Anyone who knows me knows I am a straight talker, but it is a fact, highlighted by the Plain English Society, that senior police officers have to understand the type of language used in the advert.
"What I want from our next chief constable [is] someone who can talk to politicians and judges as easily as they can their own staff and members of the public."
The deadline for applications is 1 June and the job's salary will be up to Â£150,000.

The bond, which will pay a fixed gross rate of interest of 6.50% a year until 2022, was on sale from 24 April to 6 May.
David Armstrong, the club's chief executive, said the response had been "very positive" and offered stability for the club's future.
Wasps play in the Aviva Premiership at the Ricoh Arena in Coventry.
The club moved to the 32,600-seater stadium from Adams Park, High Wycombe, in December 2014.
"The funds raised [from bond sales] will enable us to restructure our balance sheet and pay down our existing debt, including the loans we acquired with the Ricoh Arena," Mr Armstrong said.
"We now have a solid foundation for the long-term future of the club and look forward to the future with confidence."
Minimum initial investment in the bond was £2,000 - which, like any investment, has risks involved. There are plans for it to be tradable on the London Stock Exchange's Order Book for Retail Bonds.
The bonds will be guaranteed by the two key operating companies, Wasps Holdings and Arena Coventry Ltd, including the Ricoh Arena.
Interest will be paid on 13 November and 13 May in each year with the investment due to be paid back in full on 13 May, 2022. Trading in the bonds is earmarked to start on 14 May.
Opener Arun Harinath hit an unbeaten century as promoted Surrey avoided the prospect of an innings defeat on day three against Notts at Trent Bridge.
[NEXT_CONCEPT]
A 26-page job advert for a chief constable has been described as "ploddledegook" by the Plain English Campaign.
[NEXT_CONCEPT]
English rugby union club Wasps has reached its £35m target with the sale of its seven-year bond.