Hispanics voted nearly two to one for Democratic candidates on Tuesday just as they did in the 2010 midterm elections, a national exit poll shows. In a number of key races, however, they voted more heavily Republican, pointing to a strategy for Republicans in the presidential contest in 2016.

In the Senate race in Colorado, for example, where Latinos make up 14 percent of voters, a conservative Republican, Cory Gardner, took the seat of the incumbent Democrat, Mark Udall, in what analysts from both parties called a Republican playbook on how to blunt the Democrats’ advantage with Hispanics. Mr. Gardner generally avoided the contentious issue of immigration but campaigned in Latino neighborhoods with a message of job creation and smaller government.

“We had better candidates this year, who were talking about the issues that people care about and doing it in a way that did not alienate any group,” said Luis G. Fortuño, the former governor of Puerto Rico who is a member of the Republican National Committee.

Republicans said the glide to re-election of two Hispanic Republican governors in states with large Hispanic populations — Susana Martinez in New Mexico and Brian Sandoval in Nevada — also showed the party’s ability to succeed with those voters when it runs strong candidates.