Conor Coady came close for Huddersfield early on when his overhit cross nearly caught out Eastwood, who could only watch the ball sail over his head, deflect off the post and go wide.
Gestede put Blackburn in front after Rhodes did well in the box to avoid three defenders and square the ball to his strike partner, whose deflected shot rolled into the net.
Jacob Butterfield pulled one back for Huddersfield before the break with an unstoppable free kick that went in off the crossbar.
Nahki Wells and Rhodes had chances for their respective sides after the break, but both players were well denied by the men between the sticks.
Huddersfield continued to press for the equaliser and it came through Joe Lolley's half-volley from the edge of the area, after Rovers failed to clear their lines.