Mbeumo’s second, which came with 96 minutes on the clock, arrived after Brentford had initially fought back from two goals down against opposition seeking a first win of the season.
George Hirst scored and set up Sammie Szmodics for Ipswich before Yoane Wissa and a Harry Clarke own goal put Frank’s men level.
Clarke, who was later sent off, conceded a penalty which Mbeumo dispatched before Liam Delap’s 86th-minute leveller off the bench seemed enough for the Suffolk club to share the spoils.
But in the sixth minute of added-time, Mbeumo whipped a cross into the area which caught Arijanet Muric flat-footed for the winner. Despite Delap crashing against the post minutes later, Brentford held on to bounce back from last week’s 2-1 defeat at Manchester United.
Speaking after the victory, Frank said: “We’re in the entertainment business so we thought we would give you something for the money. It’s easier to be on the end of the win than being Kieran (McKenna); I feel for him and he’s working as hard as me.
“I thought they were better than us in the first 40 minutes and they were up 2-0. On the flip side we were bad and it was some of the worst 40 minutes of us in the Premier League.
“We showed great mentality, great personality and it was a fantastic comeback in many ways. Football is relentless.”
Mbeumo’s double made it eight in nine matches for the season for the Cameroon international and Frank talked up the “impressive” forward who has managed to fill the boots of Ivan Toney, who transferred to Saudi Pro League in the summer.
When asked if Mbeumo should be considered one of the league’s best, Frank added: “I hope they do that. How many goals is it now, eight in nine games? That’s hugely impressive from a winger in a team in the middle of the Premier League, that’s not normal.”
The result means three successive defeats for Kieran McKenna’s promoted men and just four points from 27 so far.
Kalvin Phillips, who is on loan from Manchester City, started and played well on a day which began amid reports his deal could be terminated early.
“It’s proper proper nonsense. I learnt a while ago in football that you can write something online, it can circulate. It’s absolute nonsense, there’s been no conversations of the like,” McKenna said.
“It’s sickening to not get any points from the game, for the goal to come so late in the manner it did. The biggest feeling I hope I have on Monday will be pride.”
McKenna also added Chieo Ogbene had suffered a serious Achilles injury.