Pedro was first on the scoresheet thanks to an assist from Giroud’s Backheel.
The second goal came from Willian, curling home from 25 yards out.
Chelsea in full control going into the second leg thanks to a late third goal from teenager Callum Hudson-Odo.
Dynamo Kiev have a lot to do in the second leg, having never won a game in England they knew it would be tough.
Favourites Chelsea looking good in Europe
Maurizio Sarri’s side will be looking to repeat what they done in 2013, winning the Europa League. This would get them into the champions league this year as they currently are 6th in the Premier league.
The Blues had a strong team fielded with six changes and the likes of Eden Hazard, N’Golo Kante and Gonzalo Higuain on the bench for backup.
Pedro scored the opener when he moved in from the left and played a one-two with Giroud before placing the ball through the legs of goalkeeper Boyko.
He then missed a glorious chance to double the lead as he fired straight at the keeper from six yards from Davide Zappacosta’s cross.
Ross Barkley had a shot stopped by the goalkeeper’s legs, before Pedro had a volley and 18-yard effort saved.
After the break, the ex-Barcelona winger again tested Boyko as he cut in from the right but his low effort was stopped.
It looked at that stage like Chelsea might be going to Ukraine with only a one-goal lead, but then Willian stepped up with a free-kick which left Boyko rooted to the spot.
Hudson-Odoi scored after a pass from fellow substitute Ruben Loftus-Cheek late on to put Chelsea on the brink of the last eight.
Kepa Arrizabalaga, who kept his place in goal, was not needed to make a save, although he flapped at a cross late on.
Hudson-Odoi continues European form
Hudson-Odoi has enjoyed the Europa League this season, netting against PAOK Salonika in the group stage and at home to Malmo in the last round.
Sarri’s refusal to give the winger more game time has frustrated Chelsea fans – especially with their recent struggles – and he came on to a great ovation when he replaced Willian with 12 minutes left.
And they chanted his name after he slotted home from 16 yards out after Loftus-Cheek flicked Pedro’s cross-field pass into his path.
Match stats – Willian is free-kick king
- Chelsea have scored in each of their past 36 European games at Stamford Bridge, since a 1-0 defeat by Manchester United in the 2010-11 Champions League quarter-finals.
- They have scored four direct free-kicks in the Europa League this season, three more than any other side.
- Dynamo Kiev have not won any of their past 10 first-leg knockout matches in the Europa League (D6 L4).
- Pedro has scored two goals in his past three games for Chelsea in all competitions, as many as he managed in his 16 before that.
- Olivier Giroud has been directly involved in seven goals in his past six Europa League games for Chelsea, scoring six and assisting one.
- Since his Chelsea debut in September 2013, Willian has scored 11 direct free-kick goals in all competitions, more than any other Premier League player.
- Willian has been directly involved in a joint-high eight goals in the Europa League this season, scoring three and assisting five (level with Sebastien Haller and Munas Dabbur).
- Callum Hudson-Odoi has been directly involved in seven goals in his past seven games in all competitions for Chelsea at Stamford Bridge (four goals, three assists).