These are the only players (who played in 5 or more Tests) whose team won all the tests in their career:
Apart from Baptiste (to a limited extent), none of them had particularly distinguished Test careers. For instance, Lord Hawke was a specialist batsman whose Test batting average was under 10. While GJ Bailey was a good limited-overs batsman he made only one fifty in Tests. They were fortunate in being in the right team at the right time-which was particularly true of Eldine Baptiste: http://www.espncricinfo.com/ci/content/player/51211.html
But there were others who had even longer winning streaks at the start of their careers.
Adam Gilchrist played 96 Tests, of which his team won 73, lost 11 and drew 12. They won all of his first 15 Tests from 5 Nov 1999 to 27 Feb 2001, until Harbhajan, VVS and Dravid spoilt Australia’s party at Kolkata.
Clark’s winning streak was from 16 Mar 2006 to 2 Jan 2008, and his career figures were 18 wins, 2 losses and 4 draws. He appears to have some Indian connection as his parents were Anglo-Indians who had migrated to Australia. As in Gilchrist’s case, his successful run ended when India won against Australia. This time it was at Perth.
Bresnan’s winning streak was from 6 May 2009 to 25 May 2012. He finished with 15 wins, 4 losses and 4 draws. He is unlikely to play Tests again.
More recently, Imran Khan (II) and “Palindrome Man” Aiden Markram saw victory in each of their first 5 Tests. While the latter is still a key player for his side, the former seems to have finished with 9 Tests with 6 wins, 2 losses and 1 draw.