Chambers nodded home a soft second that will give Ten Hag something to think about when his team returns to Manchester.
Jadon Sancho's third goal of the trip had given United an early lead and when Villa's Matty Cash turned a MarcusRashford effort beyond the reach of his own keeper, it seemed victory was secured.
But substitute Leon Bailey pulled a goal back right after half-time and Chambers' effort was reward for a much improved performance by the Reds.
The signing of Argentina defender Lisandro is expected to be completed in time for him to start training with his new team mates, including Christian Eriksen, early next week. They may need him.
It is possible that Ten Hag and Gerrard will be more interested in finding out if their teams got through the game unscathed.
The pitch was left in an awful state by a lot of rain before the game.
There was a plan to fly a helicopter over the grass in an effort to dry out the surface after ground staff tried to get rid of the excess water.
That did not happen in the end, although neither set of players looked comfortable when they tried to turn and as Gerrard had his hood pulled over his head to protect himself from another rainstorm when United's second goal went in, it did not indicate he was having a great time.
Bailey curled a shot into the bottom corner at the start of the second half to improve the Villa boss' mood.
The wide player was the one who lit up.
Since missing a penalty in the Euro 2020 shoot-out defeat by Italy, the Englishman has only played once for his country.
He struggled in his debut season at Old United but, with three goals in four games, he has finished as the top scorer on the tour with Anthony Martial.
His latest effort was excellent, with Martial, Bruno and Marcus all involved before Sancho volleyed home.
Some things went United's way.
Bailey would have leveled had Harry Maguire not dived back to turn away his goal-bound effort after the Jamaican had skipped past David de Gea.
Both clubs ended their tours without a hitch.
The two-goal lead was let slip.
He said it was not possible to throw away a 2-0 lead.
The focus was the one that mattered. I don't want to blame the weather or the pitch. We have to do our job.
We have to decrease the mistakes in football. I have seen a lot of progress in the last couple of weeks.
We have to learn from what happened in the second half after we dominated the first half.
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