William Opoku scored in the second half after some brilliant work by Chencho Gyeltshen on the left flank.
The Punjab-based team's coach Khogen Singh praised the Bhutanese player who provided the assist for the winner.
"Chencho is our key player in attack. He has the pace and the quality to keep the ball."
Minerva took time to get going in the tie as Lajong dominated the proceedings in the first half.
"We had to settle down in the first half as we mostly played on grass and this is an artificial turf. The ball moves very fast. We instructed our players to keep the ball in the second half because we knew there would be pressure on us. When we were trying to contain the counters, we started getting chances."
The win wouldn't have been possible without the heroics of Rakshit Dagar in between the sticks, especially around the 80th minute when he denied Redeem Tlang and Laurence Doe to ensure his side secured three points.
"It's a great experience. It was very windy which made it difficult to stay warm in this weather for a goalkeeper. As the game went on, it was a good experience and the crowd was also very good," stated the custodian.
Bobby Nongbet had a lot to ponder with his outfit's inability to make the best of their chances.
"If we had converted those chances in the first half, the morale of the boys would have been high. It would have given us confidence. If you don't score the pressure is on us," he reasoned.
"Their (Minerva Punjab) physicality is good but my boys are also talented. We mostly try to play on the ground, but credit to Minerva Punjab. They are a good team and congrats to them," the former Royal Wahingdoh youth coach added.
Shillong Lajong now have three back-to-back away games, starting with Churchill Brothers next week where Nongbet is keen on using Gambian forward Saihou Jagne who has been training with the squad since December 2017.
"After the first match against Churchill Brothers, we will see (how Jagne fares). The only thing we have to work on is our finishing. We have to keep moving forward and work hard for the next games," he signed off.