Overnight leader Smith finished his second round with back-to-back birdies at the 17th and 18th to head into the weekend on 13 under par at Dom Pedro Victoria Golf Course.
He joined fellow morning starter Green on that mark after the Malaysian had carded seven birdies and a solitary bogey in his second-round 65.
Finn Tapio Pulkkanen and Frenchman Benjamin Hebert were one shot back in a tie for third after they each followed up opening 66s with matching 64s to remain bogey-free after 36 holes, while England's Eddie Pepperell was in a four-man group on 11 under after also carding a 64 on Friday.
Smith has been struggling with illness after catching flu last weekend but showed no sign of that out on course.
He said: "It's always tough following a round like that yesterday.
"I felt like I hit it just as good, just missed a couple more greens and didn't quite putt as well, but I was happy with the way I finished there."
With this week's event being the last chance for players to earn points to keep their DP World Tour playing privileges, several of those who needed to make the cut in order to keep their hopes alive did so.
Among them was Englishman David Horsey, who came into the week 123rd on the rankings - six adrift of the magic mark of 117.
He made eight birdies and one bogey in his 64 to make it through to the weekend and remain in with a chance.