The Nigeria international broke the deadlock in the 48th minute and an 82nd-minute own goal from Goran Milovic saw Jaime Pacheco's side claim their first victory of the season.
Costa's 20 top-flight goals this season helped Chelsea win the league title. Tianjin were promoted to the Super League last season and have Italian World Cup winner, Fabio Cannavaro as their manager.
A club statement read: "In view of the uncertainty over the opening of the new Chinese Super League season and the uncertainty over foreign aid policy, Shanghai Greenland Shenhua and Manchester United have extended the loan for the Nigerian
The forward won the Chinese Women's Super League title with Dalian Quanjian in 2017. Oshoala was also part of the Arsenal Ladies side that won the the English FA Cup crown in the 2015/2016 season.
The former Watford striker moved to Old Trafford in January from Chinese Super League side Shanghai Shenhua, initially until May 31 but had his loan extended in June after scoring five goals last season.
It was gathered that the 22-year-old completed the transfer last week after failing to report for pre-season training with the English Women's Super League outfit, Arsenal FC.
The 30-year-old looks set to leave Manchester United in the coming days, after his Chinese Super League club asked him to return ahead of the delayed restart of the season. Ighalo's loan deal with the Red Devils ends on May 31.
The former Udinese star scored ten goals in 17 games for Shanghai Shenhua following the conclusion of the 2019 Chinese Super League season a few days ago.
Some reports had claimed the 30-year-old would leave Tianjin after an injury-hit first season since moving from Stamford Bridge, with Everton leading the chase. But Mikel said he had no intention to leave the Chinese Super League.
Rohr will be delighted to see Ighalo play in a topflight football league division next season, after his Chinese Super League team, Changchun Yatai suffered relegation, at the end of the just concluded season.
Nigeria international Odion Ighalo has completed a move to Chinese Super League club Shanghai Shenhua after leaving Changchun Yatai who relegated at the end of the season.
Chinese Super League side Shanghai Shenhua have reportedly told Nigerian star Odion Ighalo to return to camp ahead of the new season scheduled for July kick-off.
The Gabon international, who scored 42 goals for club and country last season, has also received offers from the Chinese Super League, including Tianjin Quanjian.
Nigeria midfielder John Obi Mikel has become the latest big name player to join the Chinese Super League gold rush after leaving Chelsea for Tianjin Teda. .