As the runners made the turn into the home straight, Engels took the lead and made a gesture to the crowd. Rounding the bend in fourth, Beamish began his charge inside the final 100m and finished strong, leaving Engels to throw his head back in surprise as the Kiwi came flying down his outside.
At one stage earlier in the year a contender for Tokyo Olympics New Zealand team selection, Beamish won in a personal best of 3min 54.86sec, with Engels second in 3:55.41.
The great Peter Snell's World record time in Whanganui 1962 was 3min 54.4sec.
The first eight runners in what was the secondary mile of the annual classic in Eugen last week each ran sub-four miles, but the winning time would have been good enough only for last place in the feature, won by Norwegian runner and Olympic Games 1500m gold medallist Jakob Ingebrigtsen in 3:47.24, the fastest mile ever in the US.
Beamish told Oregonlive the early celebrations from Engels urged him on as he glanced at the big screen entering the final dash down the straight.
"I got to watch Craig try to celebrate with 100 to go," he said. "I had a bit left down the home stretch."
Engels took his blunder on the chin, admitting he thought he had the race in the bag.
"I just knew it would be a sit-and-kick," he said. "I thought I had it with 100 to go. I didn't have it and got outkicked."
"I still had so much fun. It is so much fun running in front of this crowd."
He also showed he was still a good sport after the race, being the first to congratulate Beamish on his win.
In January, Beamish was one of four New Zealanders to run under four minutes in the Cooks Garden Classic mile in Whanganui, including Eric Speakman, also from Hawke's Bay.