Boro climbed back into the play-off spots thanks to Marcus Haber's strike and a penalty from Lucas Akins to leave new Pools manager John Hughes still looking for his first win in charge.
Smith said: "They have a new manager and are fighting for their lives here as they showed. We scored at important times and that was the big thing for me.
"I knew it would be tough going, the goal in the first half was one of a couple of chances we had. It was a competitive game and Marcus took his goal well, stayed on the move, got ahead of the centre-back and stayed alert enough for the second ball to score.
"In the second half as it unfolded, the penalty came at a good time for us and some passages of play were a bit more fluent, but it was Hartlepool in the main who had the better possession. Saying that it was only in the latter stages when they started to press and create chances on goal.
"When you are two goals up, the emphasis changes to defending and keeping your goal intact."