Test cricket returned to the Brabourne Stadium after 36 years in front of a sparse crowd as Sri Lanka opted to bat first after skipper Kumar Sangakkara won the toss for the first time in the series.
Dilshan (51 batting) and Paranavitana (53) batted in a forthright manner and also brought up their best first wicket partnership in the rubber, 93 in 19.5 overs.
Indian off spinner Harbhajan Singh, brought in early into the attack just before the first hour, struck a big blow when he induced the left-handed Paranavitana (53) to drive and edge to Rahul Dravid at slip just 25 minutes before lunch.
The Lanka opener batted for 95 minutes and struck seven fours in his 81-ball knock.
At the break, the 33-year-old Dilshan was batting with a fluently made 51, his 14th half century, off 63 balls studded with studded with seven fours and a six.
Lanka skipper Sangakkara (10 off 20 balls) was the other unbeaten batsman.
The visitors started briskly and rattled up 65 without loss in 12 overs in the first hour of play with both the openers finding their feet in decent batting conditions.
The left-handed Paranavitana, playing in his 10th Test after making his debut in February this year against Pakistan, on-drove and square-drove S Sreesanth for fours in successive overs.
Dilshan then took Sreesanth apart in the latter's fifth over, hooking the Kerala pacer over square leg nonchalantly for a six and then pulled the bowler ferociously from outside the off stump for a four in successive balls.
The last ball of the over was flicked beautifully by the right-hander for another four prompting India captain Mahendra Singh Dhoni to introduce off spinner Harbhajan Singh just before the first hour's play ended from the Churchgate end.
Sreesanth's first spell read an unimpressive 5-0-32-0.
The other frontline spinner Pragyan Ojha later replaced Zaheer Khan, after the latter's eight-over spell in which he gave away 37 runs, when Sri Lanka were 76 without loss in 16 overs.
Dilshan then gave Ojha the charge twice to loft him straight for a four and then off-drove him for a second four in as many balls.
But Dilshan, who was not averse to playing the cut shot to balls pitched on the middle stump, had a close call twice against Harbhajan close to the interval before completing his half-century in the same over off 57 balls.
It included the hooked six off Sreesanth and seven other boundary hits for fours.