Playing with her left knee heavily strapped, Jankovic was never in serious contention against the 60th-ranked Tanasugarn. The 31-year-old Thai, playing in her 12th consecutive Wimbledon, also was treated for a lower back problem during changeovers in the second set.
After converting on match point to reach the quarterfinals of a Grand Slam for the first time, Tanasugarn covered her face with her hands and broke into tears.
Defending champion Venus Williams, meanwhile, beat Russian teenager Alisa Kleybanova 6-3, 6-4 to move closer to another potential final against sister Serena.
Williams, a four-time Wimbledon winner, nearly squandered a 5-1 lead in the second set against the 18-year-old Kleybanova. She lost nine points in a row from her third match point in the eighth game and saved three break points at 5-4 before finally closing it with a backhand volley winner.
Williams, who has not dropped a set in four matches, played out on Court 2 - nicknamed the "Graveyard of Champions' for its long history of upsets.
Two-time champion Serena Williams was up next on the same court against Bethany Mattek, the only other remaining American in the draw. The sisters also were scheduled to play doubles together on Court 2 later Monday.
Venus Williams will next face Tanasugarn, who benefited from a below-par performance from Jankovic. The Serb, who strained her knee during her third-round win last Friday over Caroline Wozniacki, played erratically and committed 19 unforced errors.
Also advancing was Chinese wild-card entry Zheng Zie, who followed up her upset of Ivanovic last week to beat 19-year-old Hungarian Agnes Szavay 6-3, 6-4. Zheng was down 4-1 in the second set and then won five games in a row before securing her first Grand Slam quarterfinal berth.
Venus Williams struggled in the final set against the 42nd-ranked Kleybanova, one of six Russian women to reach the fourth round. Williams' father, Richard Williams, left the court with the score 4-0 and missed the comeback by the Russian that made the match interesting.
Williams was broken for the first time while serving for the match at 5-2, and Kleybanova held at love in the next game. Kleybanova had three chances to break for 5-5 but couldn't capitalize and Williams finally converted on her second match point of the game.
Between them, Venus and Serena have won six of the last eight women's singles titles at Wimbledon. They're in opposite halves of the draw and could meet in the final Saturday. The Williams sisters faced each other in the 2002 and '03 finals, with Serena winning both.
Five-time defending champion Roger Federer was playing his fourth consecutive match on Centre Court against 2002 winner Lleyton Hewitt, the only other former champion to enter the men's draw.
No. 2-ranked Rafael Nadal, runner-up to Federer the last two years, was paired against No. 17 Mihhail Youzhny.
