He scored one and made the other as City took ample revenge for defeat at Hartlepool on the opening day last season.
The home team, with four players making their debuts after a busy summer, looked disjointed for much of the game and City were always slicker in every department.
Beaten play-off finalists last season, Hartlepool looked bright at the start, but their output gradually faded away and many players were anonymous as City ran them into the ground.
Windass, top scorer last season with 28 goals, opened his account after just eight minutes of the new season.
He nipped between two static defenders to head in a cross from Marc Bridge-Wilkinson.
That knocked the wind out of Hartlepool's sails, and though the home team worked hard to battle their way back, a string of corners was all they produced apart from an overhead shot by Michael Proctor that was a couple of feet wide.
They actually carved out a better chance before City's opener, Adam Boyd flicking a Michael Nelson shot over the bar from five yards out.
It was City who got the best chance before the break with Andy Cooke blasting wide from six yards.
But ten minutes after the break, City added insult to injury by doubling their lead with a classic breakaway goal.
They survived some home pressure and broke out fast for Windass to feed Bobby Petta, who raced into the box to score from 15 yards after holding off two half-hearted challenges.
That killed the game off as a contest.
Hartlepool fought hard to come back and had plenty of possession but they rarely threatened a breakthrough up front.
Their best second-half chance arrived just after the break, before City's second, when Richie Humphreys hammered in a low free-kick from 25 yards but City keeper Donovan Ricketts saved well at the foot of his right-hand post.
For a change, nobody could begrudge the City fans their chorus of "we're going to win the league" as they left the ground after the final whistle.
On this form, they just might.