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|Ajax's Klaas-Jan Huntelaar celebrates a goal against Dinamo Kiev during the Champions League football match. (Japer RUHE/ANP/AFP)|
Ajax, four-time European champions, scored all their goals in the opening period and were denied by the woodwork on two occasions in the second half.
Donny van der Beek gave Ajax a flying start after just 80 seconds.
Dusan Tadic laid the ball into his path inside the area before van der Beek's low drive squirmed beneath the body of goalkeeper Denys Boyko.
Tomasz Kedziora pulled Kiev level after 16 minutes.
From a corner, Ajax's Cameroon goalkeeper Andre Onana made a fine save to deny a powerful header from Hungarian centre-back Tamas Kadar but Tomasz Kedziora swept in the rebound from inside the six-yard box.
The Dutch were back in front after 35 minutes when a speculative drive from Moroccan midfielder Hakim Ziyech was deflected into his own goal by Kadar.
Tadic, signed from Southampton in the summer, made it 3-1 just before half-time with a smart right-foot volley from a fine Nicolas Tagliafico cross.
Ajax remained in control in the second half with Klaas Jan Huntelaar unfortunate to see a header crash back off the crossbar.
Huntelaar then had a shot well-saved by Boyko before Ziyech saw a left-foot drive hit the post.
In Budapest, AEK Athens followed up their third qualifying round victory over Celtic by taking a 2-1 lead over Vidi back to Greece for the second leg of their play-off.
Vidi, bidding to make the group stages for the first time and become just the third Hungarian side to do so, suffered a setback after just 23 minutes when Szabolcs Huszti was red-carded for a poor challenge on AEK Athens' Anastasios Bakasetas.
Viktor Klonaridis made the most of his team's one-man advantage by giving AEK the lead 10 minutes later.
Bakasetas then made it 2-0 in the 48th minute but then got himself sent-off five minutes later for a foul on Loic Nego.
Danko Lazovic brought Hungarian champions Vidi back into the match and the tie with a 68th-minute strike.
Young Boys and Dinamo Zagreb finished level 1-1 in Berne.
Kevin Mbabu gave Young Boys, bidding to get out of the play-offs for the first time after four failures, a second minute lead.
However, Mislav Orsic pulled Zagreb level five minutes before the interval.
UEFA Champions League playoff round, first leg results:
Ajax (NED) 3 Dynamo Kiev (UKR) 1
MOL Vidi (HUN) 1 AEK Athens (GRE) 2
Young Boys (SUI) 1 Dinamo Zagreb (CRO) 1