The two Young Lions showed no mercy as they fired the Blues towards a 5-0 away win - giving new boy Diego Costa a glimpse of the competition that awaits him at Stamford Bridge to become king of the striking jungle.
Bamford, a regular in Gareth Southgate's England Under-21 squad, was the first to pounce - finishing left-footed from Nathan Ake's cross midway through the opening half.
Ivanovich scores the fourth for Chelsea
Keen to show what he could do, Brown, fresh from helping his country win the European U17 Championship in May, was next to show his killer instinct.
Two minutes after coming on at half-time, he combined brilliantly with U16 international Jay Dasilva to double Chelsea's lead with a volley.
Perhaps as a show to the club's impressive young performers, the experienced duo of captain John Terry and Branislav Ivanovic got on the scoresheet to make it four - but it would be the impressive Brown who would claim the plaudits with a sweet strike from outside the box in the closing stages to seal his double.
Fellow U17 European Championship winner Dominic Solanke was among those to appear for Chelsea as a host of England youth internationals were given a chance to shine by Mourinho.
Young Lions Nat Chalobah, Lewis Baker, John Swift, Jordan Houghton, Todd Kane and goalkeeper Mitchell Beeney all played a part in the convincing victory.
With many of the club's World Cup stars still on their summer break, this group will likely be back in action on Saturday as the Blues travel to AFC Wimbledon for their next pre-season match.
