Nottingham out-half Matt Jarvis, formerly of Connacht, kicked five penalties and the score was tied 15-15 as the game approached the hour.
Johnny Holland's second penalty of the game nudged Munster A back in front with Ronan O'Mahony scoring his fifth try in the competition to seal the win before captain Barry O'Mahony set up van den Heever to secure a late bonus point.
Munster A remain in second place behind Plymouth by virtue of the English side's superior points difference heading into Saturday's final round of group stage fixtures.
Munster A travel to Stirling County and Plymouth host Nottingham with both games kicking off at 2pm. A win for Munster will see them through to the next stage either as one of the best second-placed sides or as group winners depending on the outcome of Plymouth's game.
Head Coach Peter Malone was delighted with the attitude shown against a strong Nottingham side.
"We were looking to win this game and hoped for a bonus point to keep the pressure on Plymouth and to finish like we did with those two tries after being pegged back to 15-15 was massive for us," he said.
"It really keeps us in the frame in the competition. We were going to be under massive pressure if we didn't get that fourth try.
"It was up and down, but I must commend the heart and the commitment the lads showed right to the end. It mirrors what is going on with the senior squad at the moment. There is a never-say-die attitude and hopefully it is filtering down to the whole squad."