In the survey by political scientist Ryan P Burge, 72.8% of respondents were supportive of women preaching on Sunday morning.
Eight in ten (81%) were happy to have women preach at women's conferences and 86.9% agreed they should be able to teach Sunday school.
A fifth of evangelicals aged 65 and over disagreed with women preaching, but the same proportion of 18- to 35-year-old evangelicals also opposed women in the pulpit.
Writing in the US magazine Christianity Today, Burge said the findings suggest that "for all the debates around gender and leadership roles, for years researchers have found less of a divide on the topic among the people in the pews."
It echoes the 2011 Faith Matters Survey which found that nearly two thirds of Southern Baptists (64.7%) support women preachers.
The role of women in the church remains a divisive issue. Last year, John MacArthur was criticised for attacking Beth Moore and female preachers, saying they should "go home" because there is "no case that can be made biblically for a woman preacher".