Former Hull City and Everton striker Jelavic netted six minutes from time to ensure ex-Shanghai Shenhua and Beijing Guoan coach Manzano claimed a second successive win since his return to China this month.
"The three points are crucial to both sides," said the Spaniard. "We are working hard to get away from the relegation zone, so today every player has given his best to win the game.
"This win means a lot to us. It's not easy for a team like us to win two successive games, so this is an achievement for us. We are very happy and I believe the fans are also very happy."
The result enabled Guizhou to climb up to eighth in the standings as six-times champions Guangzhou Evergrande continued to lead the way following their 2-1 win over Jiangsu Suning.
Brazilian striker Alan scored twice for Luiz Felipe Scolari's side, who moved on to 25 points and remain two clear of Shanghai SIPG, 3-1 winners of a fiery Shanghai derby against Shanghai Shenhua thanks to two late goals.
Wu Lei gave SIPG the lead only for Obafemi Martins to score to take the teams into the break level, but an 89th-minute goal by Hulk and an own goal from Li Yunqiu two minutes into injury time gave Andre Villas-Boas's team all three points.
"I feel very sad now, the score is unacceptable," said Shenhua coach Gustavo Poyet, who was without the injured Carlos Tevez for the fifth league game in a row.
"We had very obvious opportunities during the game but we didn't seize them due to certain reasons.
"In the last 15 minutes both teams pulled open the formation. The ones who had ability to score were meant to win the game but that didn't happen to us."
Hebei CFFC moved into third place with a 2-0 win over Liaoning Whowin while Guangzhou R&F are in fourth after Dragan Stojkovic's side went a fourth game without a win when they were held to a 2-2 draw by Beijing Guoan.
Shandong Luneng's 1-1 draw with Yanbian Funde left them in fifth place while Alexandre Pato was on target for Tianjin Quanjian as Fabio Cannavaro's side defeated Chongqing Lifan 1-0 to move up to seventh.
Brown Ideye cancelled out Sun Jie's opener as Tianjin Teda shared the points with Changchun Yatai.
(Editing by Clare Fallon)
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