Ajax were joined by Young Boys, who stunned Dinamo Zagreb 2-1 away for a 3-2 aggregate win over the Croatians, and AEK Athens who scraped a 1-1 home draw with FC Vidi after a 2-1 win in the first leg in Hungary.
Dynamo Kiev piled on the pressure in the opening 10 minutes at the Olympic stadium as Benjamin Verbic forced a good save from Ajax goalkeeper Andre Onana but the home side soon fizzled out as the visitors displayed superior skill.
The home team's keeper Denys Boyko pulled off a string of superb stops after Dusan Tadic hit the post with a 14th-minute penalty and Ajax rattled the woodwork again shortly after the break as Hakim Ziyech's free kick cannoned off the crossbar.
Boyko produced another fine save to deny Klaas Jan Huntelaar in the closing stages but Dynamo lacked any bite up front and never came close to overhauling the overall two-goal deficit.
Young Boys reached the money-spinning group stage of Europe's elite club competition for the first time after 34-year-old striker Guillaume Hoarau scored twice in two minutes midway through the second half to silence a packed Maksimir stadium.
Dinamo seemed to be in the driving seat after Bosnia winger Izet Hajrovic fired them ahead in the seventh minute, sweeping home a rebound after the visitors failed to clear a fizzing low cross by Daniel Olmo.
Former PSG hitman Hoarau levelled with a 64th-minute penalty and with the home side rattled, he turned the tie on its head when he prodded the ball home from close range after a corner was headed into his path.
AEK, who last played in the group stage in the 2006-2007 season, had a seemingly simple task after their win in Hungary but were forced to hang on in a dramatic finish of the return leg in Athens.
Petros Mantalos gave AEK a 48th-minute lead with a penalty but the Greek side skated on thin ice after Loic Nego equalised on the night with a delightful lob and the home side's Helder Lopes was sent off in the 81st minute.
In Wednesday's return legs, Salzburg are at home to Red Star Belgrade after a goalless stalemate in the Serbian capital, PSV Eindhoven defend a 3-2 lead at home against BATE Borisov while PAOK and Benfica lock horns following a 1-1 draw in Lisbon.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
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