Earlier Durham recovered from 29 for 4 with a stand of 124 in 29 overs between Manoj Prabhakar and Wayne Larkins. Prabhakar raced to 86 before edging an attempted drive to slip to give Johnson his fifth victim. Dion Nash then polished off the tail with a spell of four for two in 15 balls.
Middlesex set about building on their lead of 103 with such ferocity that they had reached 125 when Jason Pooley was second out in the 21st over.
Pooley reached 1,000 runs for the season when he was on 58, but added only six more before top-edging a sweep to square-leg.Reuse content