The Bundesliga champions went behind early after Felipe Santana scored an own goal, but a brace from Lucas Barrios and a Mario Gotze strike ensured they went in 3-1 up at the break.
Pierre De Wit pulled one back for Kaiserslautern early in the second half, but Barrios completed his hat-trick in the 56th minute to restore Dortmund's two-goal cushion before Ivan Perisic grabbed a fifth.
Klopp conceded his players struggled to play their usual game in rainy conditions at the Fritz-Walter-Stadion, but was ultimately pleased with the resolve they exhibited.
"It was not so easy for my players to perform in this weather, considering football is such a demanding sport," Klopp said after the game.
"Throughout the season, we have been good defensively but today [Saturday] we were distracted easily.
"In the end, [our display] was perfect and I am very satisfied with the outcome [of the match]."
Dortmund's win means they have equalled Bayern Munich's record points tally in a single season, meaning a draw against Freiburg next Saturday will be enough to see them get one over their rivals.