Wimbledon: Elena Baltacha crashes out
• Elena Baltacha crashed out of Wimbledon in three sets
The British number one was serving for the match in the second set but inexplicably her game fell apart and she could not recover against an opponent positioned 24 places lower in the world rankings at 76.
It was the fifth time Baltacha has fallen at the first hurdle in nine appearances at the All England Club, completing a bitterly disappointing performance given a second-round clash with 11th seed Marion Bartoli was there for the taking.
Baltacha was in full control during a one-sided first set, making inroads into Martic's serve in the opening game.
The 26-year-old breezed through her own service but was troubled in the sixth, finding the net to concede break point that she saved with a blistering ace.
The wobble over, she cranked up the power with a blistering backhand and a second ace to leaving Martic flailing at air.
By the seventh game Martic had made nine unforced errors to Baltacha's one, and two further break points followed, on the second of which she was blasted out of contention.
Serving for the set, Baltacha easily secured three game-winning points before Martic found the net on the third.
Play became more even in the second set, a wonderful rally on the fifth game sending both players scampering across court before Baltacha buried a pinpoint forehand.
Martic crumbled once more when the break point eventually came, firing long to put Baltacha in the driving seat.
But the 19-year-old Croatian was offering stiffer resistance than in the first set and in the 10th game, with Baltacha serving for the match, she was offered a glimmer of hope.
Baltacha fell to pieces, saving one break point with a powerful serve but then losing a second when she was outmanoeuvred by her opponent.
Worse was to come in the 12th when Martic capitalised on Baltacha's now-troubled serve to claim two set points, the second of which the Briton fired into the net to concede the set 7-5.
Her confidence growing, Martic attacked Baltacha's serve early in the decisive set and produced one unplayable forehand.
Baltacha conceded break point when she hit the net and then surrendered the game in the same manner, before finding herself in trouble once again in the fourth.
Martic remained in control and Baltacha continued to falter when serving to stay in the set in the eighth game.
A superb passing shot from Martic set up match point but her range deserted her and she hit long to squander the opportunity.
Three more match points followed in the ninth game and Martic prevailed on the third of them when a blistering serve produced a long return.