City looked in danger of falling seven points adrift of leaders Chelsea after James Milner was sent off in the first half and then Shane Long broke the deadlock for West Brom.
But Dzeko equalised within 60 seconds of entering the action with 20 minutes left and then in injury time snatched the winner with his sixth goal of the season.
City first-team coach Platt said: "If you look at Edin's career for Manchester City, the goals he has scored, he has got a lot of heavy goals, goals that are very important.
"I remember goals at Blackburn the season before last which more or less gave us Champions League qualification.
"You look back at last season as well and he got some vital goals. To win the league, Aguero's goal will always be the one but remember Edin equalised.
"He has been a threat all season and his form has been very good all season."
Milner was sent off for a professional foul after bringing down Long midway through the first half.
But Platt felt City deserved their victory after controlling the game for long periods despite their numerical disadvantage.
Platt, deputising at the press conference for sore throat victim Roberto Mancini, said: "Watching it live it didn't seem a goalscoring opportunity to me for the sending-off. Equally you can see why it is given.
"But we can't sit there for 70 minutes grumbling about a decision.
"For the rest of the first half we were affected by it to a certain extent and no one was controlling the game.
"We said at half-time if we keep our control and discipline, stay together, we know we can impose our play on them and in that second period we controlled the match.
"If you look at the stats of efforts on goal and possession, you wouldn't have thought we'd had a man less than them."
Platt admitted City had been tempted to substitute striker Mario Balotelli at half-time after he had been booked early on for bringing down Claudio Yacob.
Referee Mark Clattenburg then spoke to City captain Vincent Kompany after Balotelli escaped a second yellow card for a challenge on Long.
Platt said: "The temptation is there (to substitute Balotelli). He got booked inside 20 minutes.
"We looked at it at half-time but he was causing them a problem and we felt confident just by speaking to him that there was not going to be any loss of head. He looked pretty calm."
The Baggies surrendered their 100% home record and manager Steve Clarke admitted they paid the penalty for chasing the winner in the closing stages.
It was from an Albion corner that City broke clear to score their late winner.
Clarke said: "I thought we deserved something out of the game. I thought we played well, stood up to Manchester City, but they showed when they went to 10 men that they are champions for a reason.
"Credit to them, their performance with 10 men was excellent and the only feeling I have now is being disappointed to lose the game so late.
"It was maybe a bad decision to go chasing the winner rather than settling for a point.
"We still wanted to win the game. It is a mindset and characteristic we have got here and are trying to put into the players.
"We wanted to win the game but you get a corner in injury time and think you can win it. Maybe we should have been a bit more careful and maybe settled for a point."
As regards the Milner red card, Clarke admitted: "It was a marginal one. If it had gone against us, maybe I would have been disappointed."