Joe Mcleod, 20, and Cullen Coulson, 24, invaded the turf at Victoria Park in jubilation after seeing Hartlepool overturn a 2-0 deficit against Harrogate Town last October.
Their actions saw them arrested and taken to court.
Appearing side by side at Teesside Magistrates’ Court, Mcleod and Coulson both pleaded guilty to going onto the playing area at a football match under the Football Offences Act 1991.
They were fined and given three-year football banning orders which prevent them from attending or being in the area of any regulated matches in the UK.
Prosecutor Saba Shan told the court: “When [Hartlepool] scored a second goal drawing level with the opposing team Mr Mcleod climbed over the barriers and ran onto the pitch.
"He punched the air repeatedly while looking at away supporters throughout.”
He went on the pitch again along with Coulson when Hartlepool scored the third goal.
Ms Shan said Coulson gestured at away fans before quickly returning to the crowd.
The court heard other supporters also went onto the pitch.
Mcleod, of Heugh Chare, and Couson of Northgate, Hartlepool, asked the court not to make the banning orders saying they had watched Hartlepool for years.
Mcleod said: “When I went on to the pitch it was nothing to do with causing violence. It was just pure joy.”
He added he did not gesture or swear at away fans and kissed another supporter’s face.
Coulson also said he did not go on the pitch to start trouble, adding: “I’m not a violent person at all.
"It was silly. It was a momentary lapse where we got a bit excited.
"I can only apologise.”
But making the orders, District Judge Marie Mallon told them: “Although I take into account you were motivated by your joy you entered the playing area which is unacceptable and highly likely to incite further violence or disorder at football matches.”
Each was fined £200 and ordered to pay £85 costs and a £34 surcharge.