Ukraine has been unable to host games since the Russian invasion in 2022.
Security issues were raised before the game following the outbreak of war in the Middle East, although England manager Sarina Wiegman said before the match that "England have been given reassurances on safety concerns".
Laura Blindkilde Brown hit the bar in the first half, but the double European champions did not find the net until the second half, when Arsenal striker Alessia Russo scored twice in the space of four minutes.
Yana Kalinina pulled one back just before the hour for Ukraine, but England moved up a gear and two goals from Georgia Stanway, one of them from the penalty spot, and two late strikes from Jess Park sealed the win.
Their biggest rivals for direct qualification from European Group A3 to the World Cup in Brazil are world champions Spain, who kicked off against Iceland later on Tuesday.
Germany took a grip on Group A4 by thrashing Slovenia 5-0 in Dresden.
Vivien Endemann and Elisa Senss put the Germans 2-0 up within 11 minutes, but they had to wait until the start of the second half for more.
Linda Dallmann and Larissa Muehlhaus, on her debut, doubled the score with Manchester United's Lea Schueller adding a fifth.
In the other game in the group, Norway won 1-0 in Austria.
Denmark made an impressive start in Group A1 with a 3-1 home win over Serbia, while Real Madrid midfielder Filippa Angeldal scored the only goal in Sweden's 1-0 win in Italy.
In Group A2, Poland and the Netherlands drew 2-2 in Gdansk while Ireland host France later on Tuesday.
Only the winners of each of the four European 'League A' groups will qualify automatically. The other 12 teams go into play-offs, which will also involve the four League B group winners, the six group winners and the two best runners-up from League C.