The Dan Jones & Associates survey of 920 registered voters statewide was conducted for KSL-TV and the Deseret Morning News, which reported the results in a copyright story Tuesday.
It found Republican Bennett leading his Democratic challenger, former Utah Attorney General Paul Van Dam, 61-24 percent.
Democrat Matheson led Republican challenger John Swallow 58-29 percent in the 2nd U.S. House District.
Bishop, R-Utah, led Logan City Councilman Steve Thompson, a Democrat, 55-24 percent in the 1st District, and Republican Cannon led South Salt Lake City police Capt. Beau Babka 56-22 percent in the 3rd District.
The poll results "are good news for me," Matheson said. "I think running this strong shows people know I put Utah first, my constituents first, that I'm not a rubber stamp for any party."
"This is about where we expected to be," Swallow said. "We haven't run any TV (commercials), so we expected to be between 25-to-35 percentage points behind."
Swallow said he'll start running TV ads in mid-to-late September, and predicted he'll also start closing on Matheson then.
Two years ago, Matheson beat Swallow by less than 1 percentage point.
The margins of error in the survey were plus or minus 3.5 percent in the Senate race and around 6.5 percent in the House districts.