Kasich has been on the rise for weeks. He was at just 3 percent in January and 15 percent in February.
"Kasich has closed the gap considerably," pollster G. Terry Madonna said.
Madonna, who predicts a competitive Republican race, offers a caveat - higher voter turnout favors Trump, lower turnout would help Kasich.
Trump gains if people who generally don't vote turn out this year because of the attention his campaign has garnered.
Kasich gains if traditional GOP voters turn out, Madonna said, pointing to moderate Republicans in Southeastern Pennsylvania.
Kasich is picking up support from major Republicans donors in Pennsylvania who had backed U.S. Sen. Marco Rubio and former Gov. Jeb Bush, two Floridians who have dropped out of the race.
The poll of 828 likely voters was conducted from March 14 to 20. It has a margin of error of plus or minus 3.3 percent.
It found the Democratic primary for president is less competitive than the GOP.
Former U.S. Secretary of State Hillary Clinton holds a comfortable lead, 53 percent to 28 percent, over U.S. Sen. Bernie Sanders of Vermont.
Clinton also leads in hypothetical general election matchups for president in Pennsylvania over Trump (46 percent to 33 percent) and Cruz (45 percent to 35 percent).
The last Republican to win a general election for president in Pennsylvania was George H.W. Bush in 1988.
In the Democratic primary for the nomination for the U.S. Senate, former U.S. Rep. Joe Sestak of Delaware County extended his lead from 21 percent in February to 31 percent in March. Former state Environmental Secretary Katie McGinty showed little improvement, coming in at 14 percent. Braddock Mayor John Fetterman ranked at 7 percent. Joe Vodvarka, a semiretired manufacturer from Allegheny County, had no support.
McGinty, recruited into the race by establishment Democrats, has faltered despite endorsements from former Gov. Ed Rendell, Gov. Wolf, and U.S. Sen. Robert Casey Jr.
The Democratic Senatorial Campaign Committee endorsed her Wednesday.
Madonna said Sestak benefits from the name recognition he gained in his 2010 run for the U.S. Senate, when he was defeated by Pat Toomey, a Lehigh County Republican.
He noted that 46 percent of the likely Democratic voters in the poll have not made up their minds about which candidate to support. That will likely make efforts to raise name recognition through television advertising, and the money to pay for it, a deciding factor, he said.