Chelsea had the better of the contest at the Yokohama Stadium, but a late goal from Leandro Damiao earned the J-League champions a famous victory in front of a crowd of 61,012.
Both teams had their moments during a relatively uneventful opening to the contest, with the first opportunity not coming until Akihiro Ienaga fired a tame volley straight at Willy Caballero from 12 yards out.
Michy Batshuayi was the next to try his luck, firing just wide of the far post after linking up well with Mason Mount, but the Blues had to wait until the half-hour mark for another opportunity as Pedro sent a 25-yard strike just over the crossbar.
Kenedy, who is eager to impress ahead of the new campaign, volleyed marginally off target from 30 yards soon afterwards, while Mount was only denied a second goal in as many games when a defender got in the way of his shot, which was heading into the bottom corner.
Kawasaki ended the first half on top, however, with Caballero having to be alert to divert a well-struck attempt from Ienaga wide of the far post.
Lampard opted to make just five alterations at half time, with Ross Barkley and Olivier Giroud among the players introduced into the action, but it was Mount who almost put Chelsea into the lead after the restart when he curled just wide of the far post from 14 yards out.
That opening spurred Kawasaki into life and Damiao should have put the hosts into the lead in the 55th minute, only to head wide at the near post after meeting a right-wing cross.
The near miss got rid of any complacency which may have been entering Chelsea's play, and it was Barkley who began to take centre stage with a series of defence-splitting passes.
One led to Kenedy getting behind the Kawasaki defence before firing wide of the near post, before the pair again linked up in the 70th minute, only for the Brazilian to fire straight at Shota Arai.
Christian Pulisic was provided with his Chelsea debut ahead of the final quarter of the encounter having arrived late after international duty, but it was Giroud who had Chelsea's next chance from a set piece, with Arai making a fine save to his left.
Chelsea continued to push for an opening goal, seemingly comfortable that they would not concede at the other end, but Kawasaki rallied to take the lead with four minutes remaining.
Moments after hitting the crossbar with a header, Damiao was perfectly positioned at the back post to nod home from close range, with Kengo Nakamura providing a delightful cross moments after being introduced as a substitute.
KAWASAKI FRONTALE (4-2-3-1): Jung (Aarai 65'); Noborizato (Nakamura 84'), Taniguchi, Jesiel, Morita (Maguinho 92'); Tanaka (Yamamura 65'), Shimoda (Hasegawa 46'); Ienaga (Chinen 46'), Abe (Wakizaka 46'), Saito (Mawatari 46'); Kobayashi (Damiao 46')
CHELSEA (4-3-3): Caballero; Azpilicueta (Zappacosta 46'), Luiz, Zouma (Christensen 46'), Alonso (Palmieri 46'); Kovacic (Bakayoko 56'), Jorginho (Drinkwater 56'), Mount (Pulisic 65'); Pedro (Barkley 46'), Kenedy (Palmer 71'), Batshuayi (Giroud 46')