Morgan made 92 as the tourists racked up 278 for nine in the second one-day international, hitting 11 fours and two muscular sixes to reach his highest score since May 2017.
It was a crucial innings and one that ensured his side were able to withstand an exemplary show of death bowling from familiar foe Lasith Malinga, who stalled English momentum to claim five for 44.
Gloomy forecasts meant a complete reply was never likely, leaving both teams chasing early momentum after the break.
It was England who grabbed it, sealing a 31-run win on Duckworth-Lewis-Stern when the rain came at 140 for five. Woakes took three cheap wickets with the new ball and Warwickshire team-mate Stone announced himself at the other end with a stirring spell of pace bowling.
Stone was left frustrated after his debut ended in a washout but this time he took the chance to impress, rattling Niroshan Dickwella with a steepling bouncer that rapped the glove on its way to Jos Buttler’s gloves.
“They were very impressive. To get early wickets and be in such a commanding position…the bowlers did a great job,” said Morgan.
“Woakes has been doing this for quite a long time, and goes overlooked a lot of the time. He really set the tone and he made a relaxing impression early on for Olly to come in and do what he does.
“Olly bowled exactly like he has in the nets and the warm-up and that’s a really good sign; pace, got the ball moving, all done with a very calm head and that’s a good sign.”
Stone is highly rated in the England ranks and might already be established in the set-up had he not missed more than a year of cricket while recovering from ruptured cruciate ligaments in his right knee.
His ability to breach 90mph, which he has cheerfully impressed upon his team-mates in training this week, represents a tantalising prospect for selectors and is emerging as a potential bolter for next summer’s World Cup squad.
With Mark Wood and the Curran brothers, Sam and Tom, all waiting for their chance in Sri Lanka and the newly-married Liam Plunkett rejoining the squad for the last two games, tough decisions are looming.
“I don’t think you can disregard Olly from the World Cup based on today. The fact he bowls with the new ball gives him an extra string to his bow,” said Morgan.
“When a side is doing well it tends to be the case that guys are sitting out who would be in any other team.”
As for his own role in setting up the win, Morgan revealed he had to dig deep to get through a rough patch at the beginning of his innings.
“I felt terrible to start, I had a really bad 20 mins, half-hour, and I nearly ran Joe (Root) out,” he said.
“I’m not a good starter anyway, but I got past that, and felt more comfortable. As the game unfolds I find it a little bit easier to take in information, know exactly what my game plan is and go to my scoring areas.
“I am working hard to get runs every game, but obviously at the start of the series it’s trying to wrestle momentum because if you can do that it goes a long way.”