The Royals had not won at the Madejski Stadium since January while an Easter mauling at Wigan had seen them slip down to ninth place.
But Adam Le Fondre's strike and an own goal by George Friend, all in the first quarter of an hour, lifted Adkins' side back into sixth and the final play-off spot with two games remaining.
"Our destiny is in our own hands," said the Royals manager.
"We were excellent, we had passion, we had hunger, we had walking wounded out there again and all credit to them.
"We started well, got two great goals and played some good football. You saw the togetherness of the team.
"Middlesbrough are a good side so for me it's an excellent result and it puts us in the play-off positions with two tough games to come.
"We are still in the race and and everyone knows when you get to the play-offs it's anyone's game."
Reading went ahead after just nine minutes when Boro goalkeeper Dimi Konstantopoulos flapped at Jordan Obita's left-wing cross.
Garath McCleary, at the far post, stabbed the ball back across goal from where Le Fondre bundled it over the line from a yard out.
It was the striker's 14th goal of the season, and his first since he hit back-to-back home hat-tricks in January.
Five minutes later the hosts doubled their advantage when Friend inadvertently nodded another Obita cross beyond his own goalkeeper.
"Adam normally goes on a run of goals but has dried up since January, it was a nice poacher's goal as well," added Adkins.
"He got us off to a great start, from a fantastic cross by Jordan. And what a threat we looked from set-pieces."
Reading could, and probably should, have scored more but Le Fondre's header hit the crossbar and Pavel Pogrebnyak was denied a solo goal by the fingertips of Konstantopoulos.
By contrast Boro, whose already slim play-off hopes were ended at the weekend, played like they already have one foot on the beach - to the obvious annoyance of their boss Aitor Karanka.
"One team was playing for the points, the other team was playing for nothing,'' he said.
"If Reading had needed more goals they could have scored them.
"It was my fault. It's difficult when you don't play for points but I didn't choose the right players and I couldn't motivate them. As a player I was competitive and I want competitive players."