England slipped to 63 for four on a tricky Edgbaston surface, where timing proved difficult, but Capsey was a reassuring presence despite the 17-year-old only making her international debut last Saturday.
Sporting a shiner having top-edged a ball into her face while warming up in the nets, Capsey shrugged off the issue to top-score with 44 off 45 balls as England overhauled their target after 17.1 overs.
Capsey was stumped attempting to hit the winning runs but Maia Bouchier did so off the very next delivery to finish on 21 not out as England made an ideal start to their Group B campaign.
While Capsey, one of seven England players aged 24 or under, has already developed a reputation for her big-hitting, the teenager showed her maturity by finding the gaps and milking Sri Lanka’s coterie of spinners for ones and twos alongside Bouchier, who was a capable foil in a crucial 42-run stand.
Nat Sciver, deputising as England captain in the absence of the injured Heather Knight, said: “Alice is very stubborn.
“She got hit in the face and other people might not have wanted to continue, it’s hard to get her off the pitch.
“I’ve not seen an innings like that from her. We’ve seen a very explosive sign of her batting but she was very calm and collected here.”
Cricket is back at the Games after 24 years and while a men’s 50-over tournament was held in Kuala Lumpur, this event in Birmingham which started on Friday is Twenty20 and exclusively for women, with England participating for the first time having declined to send a team to Malaysia in 1998.
They had a fraught couple of hours in the build-up to their tournament opener with their kit bags arriving late but they made a terrific start as Katherine Brunt celebrated her 100th T20 by trapping opener Vishmi Gunaratne in front with the first ball of the match after Sri Lanka had won the toss.
Sri Lanka, the lowest of the seven ranked teams at the Games, lost wickets at regular intervals which undermined their hopes as they posted 106 for nine, with Sophie Ecclestone justifying her status as the world’s top-ranked bowler – in both one-day internationals and T20s – by taking three for 25.
Issy Wong showed off her turn of pace in a double-wicket maiden on her home ground while Freya Kemp, 17, took two for 14 as England restricted Sri Lanka to what looked an under-par score.
England had to overcome a few nervy moments with the bat and their situation might have become more problematic had Gunaratne held on to a low chance at short fine leg after Capsey had top-edged a sweep on 17.
But, as Sciver reflected, the win was the most important thing, as she added: “We did what we had to do, really.
“It was really, really special. Walking out on the pitch, I felt everyone needed to take a moment. We had a little bit of chaos in the warm-up so we had to get everyone to focus on what they’re doing.
“Cricket’s actually the easy part, the other things in the background are harder.”
England next take on South Africa, who suffered a 13-run defeat against New Zealand earlier in the day.