Massachusetts is on course to elect its first woman and first gay governor after Maura Healey won the Democratic primary on Tuesday and a Trump-backed candidate, Geoff Diehl, won the Republican contest to face her.

Healey, the state attorney general, said: “I am honored to receive the Democratic nomination … Together, we’re going to win in November and build a Massachusetts that works for everyone.”

Massachusetts has a long record of electing moderate Republicans. Only one Democrat – Deval Patrick, from 2007 to 2015 – having been governor since 1991.

Healey, a former college and professional basketball player, has been attorney general since 2015. Polls give her huge leads over Diehl.

The Republican backs Trump’s lie that his defeat by Joe Biden in the 2020 election was the result of electoral fraud, opposed the extension of mail-in voting, opposed public health mandates in the Covid pandemic and supports the supreme court decision overturning Roe v Wade, the 1973 ruling that guaranteed the right to abortion.

The abortion issue alone has driven electoral successes that have Democrats hoping they can prosper in the midterm elections.

On Monday, Trump – the de facto leader of a party dominated by supporters Biden has called “semi-fascist” – told Massachusetts Republicans that Diehl would push back against “ultraliberal extremists” and “rule your state with an iron fist”.

In Dorchester the next day, Healey told supporters “the choice in this election could not be more clear” and said Republicans wanted to “bring Trumpism to Massachusetts”. She promised to be “a governor as tough as the state she serves”.

The current governor, Charlie Baker, worked to protect abortion rights and combat the climate crisis and backed Donald Trump’s impeachment over the Capitol attack. He faced defeat in a party dominated by Trump and chose not to run for a third term.

Healey seems all but assured of victory. The polling website fivethirtyeight.com rates Massachusetts as the state most likely to swap a Republican governor for a Democrat, “just [ahead of] Maryland, another blue state where a moderate Republican is retiring and Republicans have nominated a diehard Trump supporter to replace him”.

Elizabeth Warren, the Massachusetts US senator who beat Diehl for re-election in 2018, said on Tuesday: “Woo-hoo! I’ve seen firsthand how Maura Healey has the experience, keen policy knowledge, and steadfast commitment to deliver results for Massachusetts – and now she’s one step closer to shattering a glass ceiling as our next governor.”

Healey is set to be the second woman to govern Massachusetts but the first elected to the office. In 2001, Jane Swift, a Republican, took over from Paul Cellucci when he became US ambassador to Greece. Swift was succeeded by Mitt Romney, who became the 2012 Republican nominee for president and is now a senator from Utah.

The Democratic candidate for governor in Oregon, Tina Kotek, is also gay. If elected, she and Healey will be the first gay women to govern US states.