The pair put on 336 before being parted in the first Test against Zimbabwe at the Harare Sports Ground on Monday.
The tourists went on to 6-447 before declaring midway through day three with Chanderpaul unbeaten on 207. Captain Brathwaite had made 182.
At the close Zimbabwe were 3-114, still 333 runs behind.
Chanderpaul, 26, is the son of former West Indies batsman Shivnarine Chanderpaul. This, his maiden Test century in his third match, surpassed the 203 his father made twice, each time unbeaten in his 164-Test career.
"Congrats to Tage on his maiden century, good to see him convert it to a double," former captain and current teamamte Jason Holder said. "Well played to the captain as well. It was a really good partnership. Good to see them not only lay down the foundation but also take it really deep."
Rain meant just 89 overs were possible on the first two days of the match after West Indies had opted to bat, but the visitors accelerated the scoring on Monday.
The stand beat the previous record of 298 set by Gordon Greenidge and Desmond Haynes against England at St John's, Antigua, in 1990.
The partnership was broken when Brathwaite was out leg before wicket attempting a sweep against left-arm spinner Wellington Masakadza. It was his 12th Test century.
Legspinner Brandon Mavuta then took 5-42 as West Indies went for quick runs with mixed success, Mavuta finishing with 5-140 having bowled 41 of the innings' 143 overs.
"It's about patience and persistence, and today it paid off," Mavuta said. "I'm quite happy to be back in the team, and to be in the position we are. I'm pretty chuffed to contribute."
Zimbabwe started in reply, posting 61 for their opening partnership before Tanunurwa Makoni (33) nicked Alzarri Joseph to first slip.
Gudakesh Motie then dismissed Chamu Chibhabha (nine) and, with the final ball of the day, Brathwaite bowled Craig Ervine (13). Opener Innocent Kaia remained unbeaten on 59.
With two days to force a win, weather permitting, Holder added: "I don't want to talk about the team plan, we just need wickets. We need to be ruthless."