The former world number beat Zahlavova-Strycova, 6-3, 6-2, with her opponent also playing in her first major tournament final.
Although Ivanovic started shakily for the second day in succession, and dropped serve immediately, she recovered quickly, her heavy ground strokes and willingness to attack soon dominating her unseeded opponent.
It suggested that, at 26, not only can she adapt to a variable surface, but underlined this as her best year so far since 2008.
It was Ivanovic's 37th win and her third title of the year, putting her level with Serena Williams' and Maria Sharapova's three.
The Serb couldn't contain her happiness at conquering her doubts about playing on grass. ''On grass you really don't have time to hesitate,'' she said.
''I tried to shorten my swing and move forwards. You really have to go after your shots. It's important to be clear in your mind.''
Ivanovic will move up to world number 11, well positioned to make another move during Wimbledon, which would lift her back into the top ten for the first time in five years.
If she needed an omen suggesting she might continue this streak into the grass court Grand Slam, which starts in eight days, it came with the holding her latest trophy - the Maud Watson Cup, the same one as that presented to the English woman after she won the first ever Wimbledon, in 1884.
Could Ivanovic actually win the game's oldest title? She was understandably cautious. ''It's exciting and a new challenge,'' she said, ''just knowing that it's never over and you always have a chance.''