James Tindall shot powerfully from the top of the circle but after hitting the stick of Pillay the ball went off the Indian territory. Middleton seized the opportunity after the ball bobbled off Sandeep Singh's stick and swept home.
The slippery conditions made things difficult for the players as India began to reassert themselves in the match. Indian forwards, though, blew several opportunities.
With the rain easing, India missed a sharp chance to equalise as Prabodh Tirkey hit the ball over the goalpost.
India had another chance to restore parity six minutes into the second half when Fair saved a low and angular dragflick by Sandeep.
Prabhjot and Tushar Khandker then failed to latch on to a Prabodh set-up inside the circle.
With the clock running down, Richard Smith made sure of an English victory when he smashed home from beyond the penalty spot off a corner rebound in the 68th minute.
The second Test will be played Friday night.