The Chargers blew the doors off early, racing out to a 10-0 lead in the first quarter at Arrowhead Stadium.
Kansas City finally got on the scoreboard at the start of the second quarter when Patrick Mahomes connected with Jerick McKinnon on a short touchdown reception.
That was the end of the scoring for the first half, with both sides then trading touchdowns to open the second.
Herbert found Mike Williams in the end zone before he had a pass picked off and returned for six.
A Chiefs field goal late in the third quarter tied the scores and ensured a grandstand finish.
Things took a sour turn for the Chargers in the opening drive of the fourth quarter when Herbert was tackled while delivering a throw and forced from the field with an apparent rib injury.
Chiefs kicker Matt Ammendola then looked to have wrapped up the result for Kansas City when he converted on a 31-yard attempt.
However, Herbert bravely returned to the field and led an 11-play drive that ended with a touchdown to Joshua Palmer to keep the game alive with just over a minute to go.
Unfortunately the Chargers were unable to beat the clock as the Chiefs secured back-to-back wins to start the season.
Mahomes finished with two touchdowns and 235 yards, while Herbert posted 334 yards and three touchdowns in the losing effort.