With his side one up at halftime, United player-coach Venema called on his players to go up a gear.
Within the first five minutes of the second half, the Port Hill goalkeeper came out to pick up a ball that had been played in from United's midfield to the left-hand side of the penalty area.
In trying to get a counter-attack going quickly, the 'keeper mis-hit his kick.
Venema, in the holding midfield position, moved on to the ball from halfway, trapped it around the edge of the centre-circle and struck it with the right-boot laces from 35 metres. It went in at the top right corner.
That wasn't the first time Venema had scored such a goal.
Playing for Team Gisborne a few years ago, he scored in similar circumstances against Maycenvale.
Ten minutes after Saturday's goal, Venema came off for Sam Royston, who made an impact on the right wing, several times getting to the byline and crossing.
Port Hill came back at United, pressing until the end. Ten minutes from time they came close to scoring but Higham cleared off the line.
Higham and Mal Scammell were “awesome” in the middle of defence for United, Venema said.
Corey Adams shone in his attacking midfield role and Josh Harris was lively out on the left.
Venema said he was pleased that when United went 2-0 up they continued trying to play constructive football.
“We kept the ball for quite long periods,” he said.
“I was really impressed, because the ground was muddy.”
The competition is entering its final stages.
United's closest rivals, Maycenvale and Napier City Rovers Seconds, also won at the weekend, but United — by beating Port Hill — have reduced the title race from four runners to three.
Gisborne United have a game in hand on Maycenvale and City Rovers but arguably the toughest run-in.
On Saturday, United play City Rovers at Harry Barker Reserve, then they play Taradale away on July 3, Maycenvale in Gisborne on July 10 and Western Rangers in Gisborne on July 17.
The game against United on July 10 will be Maycenvale's last league game of the season. This Saturday they are away to Western Rangers and on July 3, home to Napier Marist Seconds.
After this weekend, City Rovers Seconds will be at home to Port Hill on July 3 and away to Havelock North Wanderers Seconds on July 10.