Sunderland were 1-0 ahead at the Stadium of Light when they were given a spot-kick as a result of Juan Cala pulling back Connor Wickham.
Dowd initially allowed play to continue before bringing the game back and pointing to the penalty spot after Sunderland had failed to gain an advantage.
Cala was sent off and Fabio Borini doubled the hosts' lead from 12 yards before Sunderland added a further two second-half goals to move out of the bottom three.
After seeing his team claim a crucial victory in their battle to stay in the Premier League, Sunderland head coach Poyet praised Dowd for his decision-making.
"It’s the best decision I've ever seen from a referee in my life," said the Uruguayan. "If we really want to stop players going down easily, this is the way.
"He's done what we all wanted but for some reason had not been possible (in the past)."
Poyet pointed to a recent incident involving West Ham's Matt Jarvis, who was denied a penalty against Arsenal after staying on his feet following a challenge from Bacary Sagna.
"Definitely Jarvis helped us a lot, because after that incident we were talking about these actions and today we got what everyone was expecting," added Poyet.
Sunderland are now out of the relegation zone and have a game in hand on the bottom three, yet Poyet insists his side must maintain their focus.
"We've done everything but done nothing," he added. "There are still games to play, and everything can change.
"We have put ourselves in the best position possible.
"We're getting the breaks and maybe we're getting them at the right time, at the end.
"It's very easy for me to pick the team now, which is credit to the players who have been there week-in, week-out. Let's see if we can finish well."
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