Bruno Fernandes scored an injury-time penalty in the 100th minute to earn Manchester United a remarkable 3-2 victory on Saturday against Brighton & Hove Albion.
In the evening kick-off, Chelsea battled back from 3-0 down to rescue a point in a 3-3 draw against West Bromwich Albion after Tammy Abraham scored an injury-time equaliser.
And Everton stayed perfect after three games after another questionable penalty decision gave them a 2-1 success at Crystal Palace and top spot in the Premier League.
Two goals from West Brom striker Callum Robinson and a simple tap in from Kyle Bartley saw the newly promoted side earn a 3-0 lead over Chelsea at half-time.
One of Lampard's newest signings in Brazilian defender Thiago Silva was at fault for Robinson's second goal as he made a mistake on his debut.
The former Paris Saint-Germain player let the ball run through to Robinson again in the 25th minute, which allowed the striker another confident finish.
Two minutes later, Lampard was not impressed as Bartley was handed an easy strike unmarked at the far post from a corner.
"It was three defensive mistakes for three goals," said Chelsea boss Frank Lampard.
Mason Mount's long-range strike in the second half kick-started the comeback before Callum Hudson-Odoi struck in the 70th minute and Abraham scored in the third minute of injury-time to complete the turnaround for the Blues.
Dominic Calvert-Lewin continued his scoring streak with his fifth goal in the 10th minute for Everton before Palace's Cheikhou Kouyate levelled the scores.
There was controversy before half-time when Everton were awarded a penalty following a video assistant (VAR) review that decided there was a handball from Joel Ward, even though his arm was down by his waist.
"A really good game destroyed by a decision," said disappointed Crystal Palace manager Roy Hodgson in summary.
"The referee doesn't think it is handball either. He doesn't want to give it but has to because that's what he is told to do.
"We have lost in a way I find totally unacceptable."
Brazilian midfielder Richarlison confidently dispatched the decisive kick.
Neal Maupay gave Brighton the lead against United with a 40th-minute penalty after Fernandes brought down Tariq Lamptey in the box, but a Lewis Dunk own-goal soon restored parity before half-time.
It was a game filled with dramatic moments. Aside from the five goals, there were two more United goals disallowed and one penalty decision overturned. Brighton were left to rue their bad luck with the goalposts.
Marcus Rashford remained composed under pressure to finish off a fine solo effort to put Ole Gunnar Solskjaer's side ahead.
Brighton hit the post five times but their luck finally turned when Solly March nodded in a free header to level the scores again in the sixth minute of added time.
Referee Chris Kavanagh had blown his whistle for full-time but VAR asked for a video check on a handball by Brighton striker Maupay after he raised his arms while defending a header from Maguire.
Maupay had his head in his hands and could not watch as Fernandes ran away to celebrate a match-winning penalty as the referee blew the final whistle a second time.
"We got away with one. Maybe one point we deserved, we didn't deserve more," United manager Solskjaer said.
Danny Ings earned Southampton its first points of the season by scoring the only goal in a win over former club Burnley in the English Premier League on Saturday.
The England striker, who finished one goal behind Golden Boot winner Jamie Vardy's 23 last season, made it three in three games for the new campaign by netting in the fifth minute at Turf Moor.
Australian Associated Press