Mayra Ramirez put Chelsea into a first-half lead on her European club debut before Chasity Grant equalised for Ajax in the second half. Chelsea prevailed 4-1 on aggregate following a 3-0 win in the first leg in Amsterdam.
Ajax nearly took the lead in the opening 20 minutes when goalkeeper Zecira Musovic had her clearance charged down by Tiny Hoekstra, but the ball rolled against the post and went agonisingly wide.
Just after the half-hour mark, Ramirez opened her Champions League account with a composed finish after being set free by Guro Reiten.
Now four goals to the good, Emma Hayes' side looked set to cruise into the final four.
Grant put a dampener on the night for Chelsea when she ran on to Hoekstra's through ball and her slightly scuffed finish squirmed its way through Musovic.
With the score level on the night, Chelsea's aggregate lead was insurmountable for Ajax although Musovic did redeem herself in the last 10 minutes when she made excellent fingertip saves to deny Romee Leuchter and then Danique Tolhoek.
Earlier in the day, Lyon progressed to the semi-finals after brushing aside Benfica 4-1 courtesy of a brace from Delphine Cascarino and a Kadidiatou Diani strike.
Leading 2-1 on aggregate after the first-leg, eight-times titleholders Lyon bettered that score at the Groupama Stadium to claim the tie 6-2.
