Ferrer matched the record of Australia's Roy Emerson, who won the Auckland singles title in 1960, '65, '66 and '67.
Spain's Ferrer took the title for the first time in 2007.
Ferrer received an email from Emerson just before the final, wishing him well in his effort to equal his record.
The Spaniard, who heads to the Australian Open, said he would return in 2014 to try for a record fifth win.
Saturday's win gave Ferrer the 19th singles title of his career and his eighth in the past 12 months.
His win in Auckland last January gave him the first of seven singles titles he won in eight finals appearances in 2012.
Kohlschreiber, ranked No. 19, was attempting to win the Heineken Open for the second time after his victory in 2008 and to add the eighth singles title of his career.
Kohlschreiber dominated early, serving strongly and returning aggressively. He broke Ferrer's serve in the third game of the opening set and didn't concede a point on serve until the eighth game when he was broken to allow Ferrer to even the set at 4-4.
Kohlschreiber broke again and had a set point as he served for the match at 5-4. But he faltered, dropped serve again and saw Ferrer take the set into a tiebreak.
Ferrer gained an early mini break and held it, winning the first set in 53 minutes.
Kohlschreiber's spirits seemed to sag after that setback. He wasn't able to serve as forcefully in the second set, or to challenge Ferrer's increasing confidence on his own serve.
Ferrer broke Kohlschreiber in the third, fifth and seventh games, to take the second set in only 24 minutes. While Kohlschreiber served five aces to none and while both players won around 65 percent of points on first serve, the German had an increasing number of unforced errors.
He made 26 in the first set and 41 in the match while Ferrer, after his slow start, was accurate and consistent.
"I'm so happy," Ferrer said. "It was amazing for me to win here four times. Now I can say this is my favorite tournament."
Kohlschreiber will still head to the Australian Open with confidence after reaching the Auckland final for the second time.
"I had a very good start," he said. "It's very hard to play against David, he never gives up.
"He gives you all the time one more shot to play. I think I still played unbelievable. I didn't take the first set and he raised his level and I dropped a bit which is why the second set went too fast."