Chelsea, last season's beaten finalists, trailed to Lucy Staniforth's well-placed penalty after Claire Rafferty fouled Danielle Brown.
But Bachmann's sweet finish levelled the scores and she scored again after a slick one-two with Karen Carney.
Two Blundell strikes made it 4-1 before Drew Spence's header sealed the win.
The draw for the semi-finals will take place live on BBC Radio 5 Live at 14:45 BST on Monday, 27 March.
Ramona Bachmann and Hannah Blundell both scored twice as Chelsea Ladies hit back to beat Sunderland Ladies and ease into the Women's FA Cup semi-finals.