The first meaningful chance of the half was carved out by the visitors as Robert Snodgrass sent over a cross from the left for Ryan Bennett, but the defender sent his headed effort straight at Brad Jones from close range.
Bennett's failure to convert that opportunity was punished with 26 minutes played. Suarez gained possession on the edge of the area and when he picked out Henderson, the former Sunderland midfielder beat Mark Bunn with a powerful shot from 20 yards out.
Having opened the scoring, the hosting Reds began to take control of the fixture and they went on to double their advantage nine minutes before the break.
Liverpool continued to dominate proceedings, but they were unable to find a third goal before the half-time whistle.