Diego Simeone’s side struck after just 47 seconds, with Pablo Barrios finishing Alex Baena’s cross.
Lookman, introduced for Julián Álvarez in the 71st minute, tapped home the rebound eight minutes later after goalkeeper Senne Lammens saved David’s shot.
“We know how big of a win that is for us,” Lookman told CBS Sports Golazo.
“The guys put on a big performance before I came on, so it was easy to come into the team and play.”
The result extended Atlético’s winning run to five matches across all competitions, following league successes against Real Sociedad, Osasuna, Real Madrid and Alavés.
It also delivered their first points of the Champions League campaign after an opening defeat to Liverpool.
For United the defeat prolonged a torrid start to the season. Carrick’s side have made their worst Premier League opening in 40 years, collecting just six points from six games, and this result stretched their winless run to five matches.