England, ranked second in the world, were strong favourites and led 2-0 in the first quarter courtesy of goals from Giselle Ansley and Alex Danson.
Susannah Townsend then finished off Hannah Martin's run before Gurjit Kaur pulled one back from a penalty corner.
Martin netted one of her own late on as England progressed to face USA in the semi-final on Thursday.
Germany defeated hosts South Africa 1-0 in their quarter-final and will now face Argentina who beat Ireland 2-1. USA beat Japan 1-0 in their last-eight match.
England, Germany, Argentina and USA have now qualified for the World League Finals in New Zealand in November.
Media playback is not supported on this device
Ansley put England ahead from the penalty spot before Danson reacted quickest as the umpire played advantage to hammer in from close range.
India hit the post late in the second quarter and piled on the pressure before half-time but could not find the target from their penalty corners.
They were left to rue their mistakes when England grabbed a third goal - their best of the match - as Martin dribbled to the by-line and found Townsend.
India finally scored through Kaur's low flick into the bottom-right corner but Martin wrapped up an easy victory for England.
England head coach Danny Kerry missed his side's past two fixtures as he is unwell and it has been confirmed that he will not attend the squad's remaining matches.
England starting XI: Maddie Hinch (GK), Giselle Ansley, Laura Unsworth, Hollie Webb, Anna Toman, Sarah Haycroft, Emily Defroand, Susannah Townsend, Nicola White, Alex Danson (C), Sophie Bray
Subs (used): Shona McCallin, Zoe Shipperley, Grace Balsdon, Hannah Martin, Jo Hunter
Subs (not used): Amy Tennant
Find out how to get into hockey with our special guide.
England beat India 4-1 to reach the last four at the Women's Hockey World League semi-finals in Johannesburg.