"Spinners are going to have a huge role and we've got three great spinners all bowling very nicely".
Jennings, when he does get to the crease, will be under characteristic pressure to put in a big contribution.
England were boosted by a five-run penalty during Sri Lanka's innings after Roshen was deemed to have deliberately run short at one end before returning to the other in an attempt to retain the strike.
The visitors were yet to open their account after nightwatchman Jack Leach faced six balls from Dilruwan Perera in the final over of the day.
Ben Stokes (19) was promoted to bat at No.3 and was adjudged lbw to Dilruwan Perera on review after the Sri Lankans referred the original decision.
Silva, in for injured captain Dinesh Chandimal, was on 6 when Angelo Mathews fell for 20, and from there he stitched some valuable partnerships with the lower order to post a competitive total, Sri Lanka's highest in the series.
Root dominated the spinners, scoring freely to reach his 15th Test ton and first away from home since replacing Alastair Cook as skipper previous year. The pair batted without any fear of a crumbling on a Day 3 subcontinental track and took the attack to the opposition by using the sweeps to good effect.
Ben Stokes put down a hard chance at slip with Silva on 52. He slid and managed to keep the ball from crossing the boundary. He turned before completing his first run.
England dropped Akila Dananjaya when he was on 30 as Jos Buttler failed to hold onto a chance off James Anderson.
He was dropped on 53 by Pushpakumara and was the last man dismissed for a well compiled 64.
Akila eventually ended his fine knock, Root lbw as he tried to reverse sweep, and bowled Sam Curran with a attractive off-break next ball.
Earlier, Curran and Adil Rashid added 45 runs for the eighth wicket with Rashid contributing 31 runs.
"No, I didn't expect that", he said, before anointing himself the heir to a Somerset team-mate and former England opener Marcus Trescothick.
"It was crucial. Getting close to 300 was massive for us". "It was the wrong call and we took on the wrong guy. Ben Stokes has a strong arm, so we'll be cautious".
He said to limit England for a target of 200 would be ideal. "We got a nice score on the board", Curran said.
"We got a 46 runs lead, its a huge score for us when they play in the second innings".
England are 1-0 up in the three-Test series after their 211-run victory in the opening match in Galle.
Roshen Silva top-scored with 85 and enjoyed support from fellow half-centurions Dimuth Karunaratne and Dhananjaya de Silva.
Captain Joe Root (14) was bowled off an inside edge as Malinda Pushpakumara, making a return to the test XI, made an impact.