Still, despite these gains, savings are falling far short of goals. Fidelity projects that on average, families will have saved just 34 percent of their target share of overall college costs—and that target share is just 62 percent of the total price tag.
(Read more: $ave me: Coming up with $500,000 for college)
The savings rate "is improving," up from 30 percent of a smaller target share in 2012, said Keith Bernhardt, vice president of college planning at Fidelity. "The negative is that it's only 34 percent."
As for the conversations about college savings, the survey did find that parents having those early talks with their offspring are more likely to be saving for college.
But affluent families are somewhat more likely to have those conversations, according to the survey. Forty-six percent of those with incomes of over $125,000 and 49 percent with income of between $63,000 and $124,900 are having "the talk," compared with 40 percent earning less than $62,900.
It simply may be, as other studies have shown, that families better-positioned to put away money talk about the college-savings process.
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Though the relationship between talking and saving is unclear, Bernhardt said, "you're more likely to take action if you've started thinking about it and having those conversations."
(Read more: 529 rebels: alternative ways to save for college)
One reason for the pickup may be that parents are all too familiar with the burden of college debt: Thirty-six of respondents said they are still paying off their own higher-education loans.
(Read more: The college debt crisis: Special report)
Overall, the parents gave themselves a grade of B-minus for their efforts. Considering they are on track to reach only one-third of their target, that could well be called a stretch. But Bernhardt is unwilling to change the grade.
"The 34 percent suggests there is still a lot more they could do," but "we want them to feel empowered more than nerve-racked about it," he said.
The key is to get moving, Bernhardt said. "Just start saving. You don't need the perfect plan. You'll figure it out as you go."
—By CNBC's Kelley Holland. Follow her on Twitter