Midfielder Smallwood was sent off for a late challenge on Billy Knott just before half-time.
But substitute Kieran Agard came to the rescue with a 79th-minute winner - his 25th goal of the season - to move Rotherham up to third place in the table and earn a first win in four.
Agard slammed home the winner after Vale failed to clear a Joe Skarz cross, beating Sam Johnson with a right foot shot.
Gaffer Evans said afterwards: "We were all stunned by the sending-off. No Port Vale player or their manager appealed.
"This is the referee with the top marks in the country, but he was poor for both teams, particularly in the first half."
But Evans was delighted his 10 men went on to win the game.
"I am pleased with the win," he added. "It is extremely important we try to win every game we play now.
"I told the lads they were gutless and lacked energy at half-time, but some of our play in the second half was sensational.
"At times in the second half it looked as though we had 12 players on the field rather than 10."
Source PA