Mitrovic came off the bench to cancel out Timm Klose's first Norwich goal.
Dieumerci Mbokani scored three minutes later to restore the hosts' lead, but Mitrovic then converted from the spot after Gary O'Neil was penalised for handball before Olsson's winner.
Mbokani was at Brussels Airport on March 22 when two suicide bombers struck, and, along with a further attack on the metro, caused 32 deaths.
Norwich reported the 30-year-old Congo international was "unharmed but shaken".
Neil lauded Mbokani's display against the Magpies after speaking to the striker during the week.
The Scot said: "What I said to him was, whatever goes on in your personal life, off the field, you've always got football to fall back on - that's your release. Just go out, enjoy the game, play and do what you do.
"I thought he was great. His goal was magnificent and I thought his performance was magnificent. I thought he was excellent."
Olsson's goal earned back-to-back wins for Norwich for the first time since the turn of the year, when they last won at home against Southampton.
"We nearly didn't (win)," Neil said. "We scored two goals, took the lead twice and I felt deservedly so.
"But we found ourselves at 2-2 with two minutes to go and that was really frustrating for us, because I thought we were the better side.
"Martin scoring that last goal was a sweet way to win the game, but I thought it was no more than we deserved.
"If we hadn't scored that goal it would've been more difficult.
"The fact we got it gave us another two points to our tally. It's a massive two points."
And Neil's delight was not at all tempered by a dispute with a disgruntled Norwich supporter sitting near the dugouts.
"We conceded a goal for 1-1 and one of our own fans started shouting at me, which I wasn't happy with," Neil added.
"He was on the wrong side of their dugout and when we scored our second goal it was him I was running to. It wasn't anything to do with Newcastle.
"We're all fighting for the same cause. I'm sure he'll be going home as happy as anybody else now."