The hosts won Tuesday's first T20 in Southampton by 119 runs and followed it up on an overcast evening with a 14th consecutive victory over Sri Lanka in the format.
Set a target of 146 after winning the toss and opting to bowl at a murky and overcast Sophia Gardens, England had marched to 48-0 after four overs, but openers Aneurin Donald (21) and Buttler (30) then walked in quick succession for 55-2.
Big-hitting captain Harry Brook smashed three sixes in one over but went for 23, well caught by Eshan Malinga off a Wanindu Hasaranga delivery, before Tom Banton steadied the ship with a top-scoring 52 not out from 24 balls as England cantered towards another easy win with 47 balls and 7.5 overs to spare.
"Tonight was a special performance, very clinical. Sri Lanka got off to a flier, but the way we fought back with the ball was outstanding," said Brook.
"The way Dawson reads the game was outstanding, too."
Buttler reached his career 15,000 with a single and Brook said his milestone was simply ridiculous.
"Long may it continue. He has been phenomenal for 15 years and someone you want by your side and in the changing room," he added.
Sri Lanka posted 145 for 9 from their 20 overs, an improvement on their previous 135 all out in 19, with opener Pathum Nissanka hitting 37 from 21 balls.
They had carved out a promising 56-0 but lost momentum with Jamie Overton taking the first wicket with a leaping catch off Player of the Match Dawson, who took his second wicket with the next ball of the sixth over and ended with figures of 3-32.
Jofra Archer (2-34) returned for his 50th T20 cap after being rested for the first T20 of the series, with fellow seamer Josh Tongue dropping out, and took two wickets in the final over with Dushmantha Chameera bowled middle stump for a duck and Tharindu Rathnayake caught by Brook.
Sonny Baker had another excellent evening with the ball, finishing 1-15 from his four overs with a wicket maiden in the 19th.
Donald, playing on home Welsh soil after making his debut in Southampton, dropped Dasun Shanaka but made up for it with a catch three deliveries later for Dawson's third wicket.
"They were too good. We have to improve a lot, honestly, because we are not up to the mark right now," said Sri Lanka captain Charith Asalanka.
The final T20 of the three-match series is at Manchester's Old Trafford on Saturday.