Jodi defeated Hampshires Liz Bennett after the two Curtis Cup players had tied on three-under par at the end of 72 holes of regulation play.
This is incredible, its got to be my best individual win, said Jodi, who plays at Catterick and is a student at New Mexico University in the USA . It was wonderful to win last year but the field is much better this year and so its more special.
The 20-year-old also won the U21 and U23 trophies.
However, with one round to play the outcome of the championship had looked very different. Lancashires Florentyna Parker, who had been in front from the first day, had extended her lead over the field to seven shots.
She was on eight-under par while her four closest challengers were on one-under.
Alongside Jodi and Liz Bennett (Brokenhurst Manor) were English champion Hannah Barwood (Knowle) and Kerry Smith (Waterlooville).
I didnt think I had a chance, said Jodi. To be honest I went out to play for second place.
Florentyna, who also played in the Curtis Cup, was still seven-under at the turn and well clear of the field. But her lead fell away on the back nine as she dropped a series of shots and she eventually came in with an 80 and a level par total for the tournament.
Meanwhile Liz , who was playing three groups ahead, took the clubhouse lead when she returned a final round 70 for a total of three-under par. Jodi, who knew the situation, birdied the 17th to get to four-under but then dropped a shot at the 18th, where her approach found a greenside bunker.
The two golfers returned to the course for the sudden death play-off and halved holes one, two and 17 in par before coming to the 399-yard 18th where Jodi took the title with a textbook four. Liz, who had chipped impressively on the first two play-off holes, just failed to get up and down on this occasion.
At lunchtime I certainly didnt expect to be in a play-off, said Liz. I played solidly all week and Im pleased with that.
The next big date for all three Curtis Cup players comes on Monday when they return to The Berkshire, alongside five other English amateurs, to play for places in the Ricoh Womens British Open.
Gloucestershire won the U23 county team trophy, thanks to Charlotte Ellis and Hannah Barwood whose combined scores from the first two rounds totalled 287.
Next years English strokeplay championship will be an open tournament and will take place at Enmore Park, Somerset, from August 4-6.
Leading final scores
(Par 72. CSS 77, 76, 76, 76)
285 Jodi Ewart (Catterick) 70, 69, 76, 70; Liz Bennett (Brokenhurst Manor) 71, 73, 71, 70. Jodi Ewart won at the fourth extra hole.
288 Ellie Givens (Blackwell Grange) 73, 74, 72, 69; Kerry Smith (Waterlooville) 72, 70, 73, 73; Florentyna Parker (Royal Birkdale) 69, 68, 71, 80
289 Rachel Jennings (Izaak Walton) 74, 74, 72, 69
291 Charlotte Ellis (Minchinhampton) 72, 72, 74, 73
292 Emma Brown (Malton & Norton) 74, 71, 74, 73
293 Hannah Ralph (Cowdray Park) 76, 73, 74, 70; Naomi Edwards (Ganton) 71, 77, 72, 73
294 Hannah Barwood (Knowle) 70, 73, 72, 79
295 Holly Aitchison (Befordshire) 69, 76, 78, 72
296 Sian James (Bristol & Clifton) 77, 71, 72, 76; Hannah Burke (Mid-Herts) 72, 69, 76, 79
297 Laura Collin (John OGaunt) 75, 74, 71, 77
Full details and hole-by-hole scoring: www.englishwomensgolf.org