The Daggers boss operates on a shoestring budget yet saw his side keep the heat on leaders Bournemouth as Abu Ogogo's 72nd-minute winner sunk Stuart McCall's Bradford.
And after building a team made up of other clubs' rejects and a healthy dose of non-league players, don't expect Still's side to fade away as big-spending Notts County lag five points behind them.
But it was a different story for McCall's men.
They were left facing up to a second straight defeat despite matching their hosts for long spells after Michael Flynn cancelled out striker Paul Benson's opener.
That has left their promotion hopes hanging by a thread as they are nine points off the top three and McCall admitted his side deserved to lose.
The Bradford boss warned his squad he will only be happy if they win their next four games.
He said: "We didn't get to grips with them and I know a few individuals can do better.
"I'm disappointed with the goals we lost and we haven't worked their keeper enough.
"We have three of our next four games at home, and I want to be sitting here with maximum points from them."
Still could barely contain his excitement as Daggers made it 19 points out of 21 at Victoria Road this season.
He said: "When Bradford were in the Premier League, we were messing about in the Ryman League.
"For us to beat Bradford almost defies anything else that can happen in football at this level."
No one will have been more grateful to Ogogo for grabbing the winner than Benson.
The striker got his ninth of the season early on, crashing home after keeper Simon Eastwood flapped at a corner.
Flynn hit back for the visitors in style, lashing in a 25-yard volley that left Daggers keeper Tony Roberts, 40, flapping at thin air.
But within 60 seconds Benson had wasted a glorious chance to put the Daggers back in front from the spot.
John Nurse won the penalty after Zesh Rehman's crazy tackle but Benson blasted high and wide.
Former Arsenal youngster Ogogo finally grabbed the winner, stabbing home after Nurse had pulled the ball back to him.
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