McDowell had spoken prior to the tournament of reducing Martin Kaymer's lead in the Race to Dubai standings and the Northern Irishman set about his task in determined fashion.
With the first round delayed by four hours due to thunderstorms, McDowell was forced to finish his opening 18 holes on Friday morning and he posted a 65 that featured seven birdies and a bogey over the more difficult Serapong course at Sentosa Golf Club.
The 31 year old then carried his fine form over to the Tanjong layout, birdieing the first four holes before a bogey at the fifth checked his progress.
Scott, meanwhile, matched McDowell's 65 and the Australian then reeled off three birdies in a row from the third on the Tanjon course to climb into a share of the lead.
The duo head Rikard Karlberg, the Swede one-under through 15 holes of the Serapong course, Japan's Hiroshi Iwata - three under after 10 - and overnight clubhouse leaders Chris Wood and Kim Bi-o by one stroke, the latter two yet to start their second rounds.
Four players - Raphael Jacquelin, Keith Horne, Fredrik Andersson Hed and Shigeki Maruyama were at seven under par, while last week's World Golf Championships - HSBC Champions winner Francesco Molinari was in a group at six under.
Ignacio Garrido, who had completed a blistering 62 on Friday morning to lead after the first round, had slipped back into a tie for 17th on five under after playing the first 10 holes of the Serapong course in four over par.