Morgan made 92 as the tourists racked up 278-9in 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 5-44.
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 140-5.
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 as he emerges 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,” said Morgan.
“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.”
The Yorkshire pair of Jonny Bairstow and Root ensured no more early dramas after Malinga’s early dismissal of Jason Roy, with stand of 72.
Root was at his most fluent with the field up and balls new, with five of his first 15 deliveries clipped to the boundary including three in a row from Malinga.
He would have to wait 54 balls to find the ropes again but never allowed his scoring rate to drag with a combination of canny placement and hard running.
Bairstow, by contrast, never quite found his feet. The opener became only the sixth Englishman to score 1,000 ODI runs in a calendar year but when he lost his off-stump to Thisara Perera it was no great surprise.
Root benefited from Morgan’s arrival, the Irishman troubled at first by spin but always ready with a punchy riposte.
Root, already dropped on 48, had begun to tire when he chipped De Silva to cover via a leading edge – 309 runs and four games since his last dismissal.
In Sri Lanka’s reply, the contest was effectively lost at 31-4 and although Thisara (44no) led a middle-order revival, their 29-over score of 140-5 was nowhere near enough to trouble England when the rain came.