Sebastian Maier opened the scoring for one of the promotion front-runners, with the hosts themselves having missed a glorious early opportunity.
Marcel Gaus was left ruing his inability to convert from close range as, down the other end, the Hannover midfielder finished a scrappy bit of play off with a composed finish.
Kaiserslautern continued to dominate for the remainder of the half but they would not enjoy as promising a start to the second period as they did the first, with Waldemar Anton on hand to double the visitors' lead three minutes in.
The defender was in the right place at the right time to finish from a corner to make it two, before Artur Sobiech's header just past the hour wrapped things up.
However, Sobiech would add the cherry on top too, curling in a delightful fourth from the edge of the area to really seal a perfect win.
Luck in, luck out
As two of last season's most luckless sides met to open up the second division's season in Germany, Kaiserslautern's start suggested that some things just do not change - or at least not overnight.
With just six minutes on the clock, the hosts should have been ahead with an attack that threatened to send the noise levels at the Fritz-Walter-Stadion through the roof, but their lack of cutting edge was prominent once more in front of their adoring fans.
Osayamen Osawe found himself in acres of space and in behind the Hannover defence, but instead of opting to shoot himself, the forward squared to an unmarked Gaus. Even with the goal at his mercy though, the 27-year-old fired his shot right at a scrambling Philipp Tschauner, despite him appearing to have no chance of saving.
Kaiserslautern did continued their strong start when Osawe himself came close with a long range effort, but Tschauner palmed it away again and less than 10 minutes later, low and behold, they were behind.
It was a fortuitous goal for Hannover to score too, with their luck clearly in after being absent all of last term. Felix Klaus will be credited with the assist, his scuffed cross deflected into the path of Maier by a defender's touch, with Sobiech using his body well to block a defender from intercepting. First time, Maier directed the ball goalwards, with the top corner its destination as the summer signing opened his account for the club.
Coming on the counter and against the run of play, the deadlock breaker simply confirmed the fears of Kaiserslautern - that their luck still hasn't changed.
Result put beyond doubt
That sixth minute miss looked to be only more of a pivotal moment three minutes into the second half, as Hannover doubled their lead.
Again, luck perhaps played a part, with Klaus well offside as Salif Sané's headed effort was saved, but he was adjudged not to be interfering with play by affecting goalkeeper André Weis' eyeline.
Anton certainly wasn't offside though as he pounced on the parried shot and slotted in the rebound, giving the visitors a very comfortable 2-0 advantage.
This only further increased their confidence and Sobiech almost made it three before the hour, outmuscling Stipe Vucur having chased down a lost cause, but he was unable to beat the onrushing Weis.
If the result was in any doubt though, Sobiech put the game to bed with 63 minutes on the clock; a set piece again undoing Kaiserslautern.
This time is was a corner worked short, with Manuel Schmiedebach providing the delivery and Kenan Karaman heading it across goal for Sobiech to then redirect into the back of the net.
It had not been a dominant display by Hannover by any means, but more a clinical one and a well-executed away performance - all with more than 25 minutes left to play.
With the game somewhat slumping towards its finish line, Sobiech then added a top quality fourth to make the final stages worth watching. As he curled the ball into the top corner from the edge of the area, Hannover confirmed that they mean business this season.