Andoni Iraola's in-form side extended their lead through substitute Philip Billing's header and Manchester United's afternoon got even worse when Marcos Senesi nodded in the visitors' third from a corner.
The Three Lions levelled the game in the 73rd minute, after substitute Cole Palmer drilled the ball in. Mikel Oyarzabal then slid in to tuck home Marc Cucurella's low cross.
However, Bayern substitute, Javi Martinez, then scored a 104th-minute winner to leave Rakitic praising the performance of Neuer. "It's disappointing, but that's football," Rakitic told Sky Germany.
Iheanacho, who came on as a substitute, finished a Jamie Vardy's pass to reward The Foxes second-half pressure. Freddy Guilbert put Aston Villa ahead with their first shot of the game after 28 minutes.
It was a bittersweet night for PSG, as Lionel Messi made his long-awaited debut as a second half substitute, but Mbappe's excellent performance came on what could be his final appearance for the Parisian club.
Suarez, 25, joined the Gunners on loan during the January transfer window, but has only made six appearances as a substitute. Arsenal have the option to buy Suarez for £18 million when his loan deal finishes at the end of the season.
Cole Palmer appeared to have won it for City after a mostly forgettable 70 minutes in the season opener when the substitute curled in a spectacular shot.
Savinho came on as a second-half substitute as City beat Manchester United in the Community Shield game on Saturday. Guardiola was impressed by the versatility and confidence shown by the former Girona winger.
Rooney, playing at No 10, then turned the match in the second half by equalising from close range and converting a penalty after substitute Marcus Rashford had been fouled.
Substitute Alexandre Lacazette scored twice as Arsenal thumped Paris St-Germain 5-1 in Singapore. Lacazette flicked in a finish from Emile Smith-Rowe's cross and headed home his second in the friendly.