The match was goalless at the end of the first-half before sparking into life after the restart.
Coupar Angus took the lead early on in the second-half only for Wolecki Black’s side to roll their sleeves up and hit three goals to ensure all of the points.
The game was Tayport’s final of the league season and helped them go into the Quest Precision Engineering Cup final on June 4 with a spring in their step.
The Canniepairt boss said: “I’m really pleased to finish the league campaign with three points because at half-time I’d warned the players they were in danger of losing a point or two.
"I’m very pleased we came back late in the game to make sure we salvaged the three points.
"We made a change in formation which helped to put more attackers up the top end of the park.
"That contributed towards us creating chances and scoring goals.
"But credit to Coupar Angus, they made it a very difficult game for us.”
One of the standouts during the game was Tayport goalkeeper Craig Hepburn.
Not only did he do his part with a couple of saves, Wolecki Black was equally as delighted with the ‘keeper's distribution.
"He had a fantastic assist for Jamie Gill’s goal and that was a crucial one that got us 2-1 up,” added the manager.
"We scored the two goals in two minutes and that really turned the tide and gave us the confidence to see the game out.”
The end of the league season has perhaps come too soon for a Tayport side who are really hitting their stride.
Under Wolecki Black they’ve risen up the Midlands League but his arrival came just too late to sustain a title challenge.
"To be honest, I think all of the damage was done before I got in,” he said.
"We had a mountain to climb in terms of pushing up the league but we’ve managed to get up the table a few places and are in a cup final, so I’d like to think there’s been a bit of success.
"Now we need to improve the squad to continue to run of form we’ve been on.
"We also need to make sure we win games we shouldn't be dropping points at.