Mr Murdoch won 51% of votes cast by independent shareholders at the annual general meeting - up from 49% past year.
The Institute of Directors had urged Sky top consider replacing Murdoch as chair if he had fallen below 50 percent support of shareholders not affiliated with Fox.
"There´s nothing wrong with Mr Murdoch - but it is because of the name".
Some institutional shareholders had criticized Murdoch's appointment as chairman, arguing that could pose a conflict of interest given his role as CEO of Sky's largest shareholder.
In a stock exchange announcement detailing the AGM vote, Sky said: "The board is pleased that the majority of resolutions have been passed with a high level of support from shareholders".
Fox's US$15 billion bid for Sky is now with United Kingdom competition watchdogs.
In response to the question about the Fox News scandal, Darroch said the "whole board are incredibly supportive and behind Sky" and that it wanted to make a "broader contribution" to society.
Ofcom chief executive Sharon White has said she is "absolutely confident" that the broadcasting regulator was right in ruling that the planned purchase of Sky by Rupert Murdoch's 21 Century Fox would not undermine its broadcasting standards.
The Competition and Markets Authority (CMA) says it will investigate how 21st Century Fox's proposed takeover of Sky would affect media plurality and broadcasting standards in the UK.
Asked by members of the Culture, Media and Sport Select Committee about that decision, Ms White said Ofcom had carried out a thorough review of recent activity at both 21st Century Fox and also at News Corporation - the owner of The Sun, The Times and The Sunday Times - which until 2013 were both part of the same company.
Its bid, which is strongly opposed by some lawmakers and is subject to lengthy regulatory scrutiny, hangs over the European pay-TV group, which reported quarterly results earlier on Thursday.
Like-for-like revenues during the three months to the end of September were £3.3bn, up 5.5% on the same period a year ago, while EBITDA (earnings before interest, taxation, depreciation and amortisation) rose by 11% to £582m. The pay package handed to Sky's chief executive, Jeremy Darroch, quadrupled to more than £16m in the year to the end of June, despite a hefty fall in annual profits at the broadcaster's United Kingdom and Ireland business.
Mr Darroch said it was a strong start to the new financial year: "Against the backdrop of pressure on consumer spending and lower spend on United Kingdom television advertising, we were particularly pleased with our own EBITDA growth of 15% in our established business".
He said the company was seeing good demand for its flagship Sky Q product as well as for its streaming service Now TV.
He added: "Game of Thrones has become the most watched series ever on Sky".
Shares in 21st Century Fox were flat at $25.50 in light-volume trading.