Eibar midfielder Pape Diop was sent off for the second time this season with 18 minutes remaining, but Rodrigues' later header gave them three vital points in injury time. The visitors also had to thank goalkeeper Marco Dmitrovic for an excellent penalty save with the score at 1-1.
"They're the best team in the league, and proved it today," said Shandong coach Luka Sjekloca. Enditem
The 29-year-old has been deployed by Toffees manager Carlo Ancelotti as a free-roaming No. 10, having been shunted out wide or used in a deeper midfield role during his limited opportunities for Real Madrid last season.
Han Peng's direct corner goal in the 47th minute and Temwa Chawinga's goal in the 81st minute helped Wuhan secure a 4-0 victory, despite a missed penalty by Beatriz Zaneratto Joao in the 78th minute.
"We haven't played for a long time. We played a bit tight today, but took our chance at last," said Shanxi coach Li Ge.
"I executed the race well despite not being fully fit. I have a hamstring injury that I want to manage when I take a break, this being the last event this season. It feels good to end the season on a winning tone, especially at home, having won the Diamond League races in Monaco and Stockholm.
FC Barcelona's positive start under Ronald Koeman had produced two wins and seven goals without reply in their first two matches of the season, but that positive start was halted as they were held 1-1 at home to Sevilla on Sunday evening.
Although it is still very early days, the signs are much better at FC Barcelona than many expected before the season started. Ronald Koeman's team has won its first two games with ease, netting a total of seven goals without conceding and the image on the pitch has been much better than the side that looked sad and tired during Quique Setien's time in charge.
Next up for Halep is another 19-year-old youngster, Iga Swiatek of Poland, whom Halep defeated in the round of 16 here last year.
Lo Celso did not train with his Albiceleste teammates on Monday after failing to recover from the muscle strain that kept him out of Tottenham's 6-1 victory at Manchester United on Sunday.
Meanwhile Southampton claimed a routine 2-0 victory at home to West Bromwich Albion, who is still searching for its first win of the campaign.