Gosport and Fareham Inshore Rescue Service (GAFIRS) answered the Mayday call around 3.20pm after the skipper reported flames on board the 38ft boat.
Both people were recovered to safety before the vessel was towed away from the busy shipping channel and into shallow water.
With flames totally engulfing the cabin the lifeboat crew deployed an anchor, with help from Bembridge RNLI Lifeboat, to prevent drifting and stop the boat becoming a greater hazard.
Duty Coxswain Pete Byford said ‘Thankfully we were on duty with the lifeboat and out training as it was only a matter of minutes from our arrival until the vessel was completely engulfed in flames.
‘The crew on board the vessel had done everything they should: immediately calling for help, wearing their PPE equipment and being ready for the Lifeboat to arrive.’
Bembridge RNLI Lifeboat took the casualties into Chichester Harbour, where the vessel had been based.
GAFIRS kept passing vessels at a safe distance as flares and gas cylinders on board exploded.
A duty fire tug, SD Independent, came from Portsmouth harbour to fight the fire but the vessel it was unable to be saved and sank shortly afterwards.
GAFIRS assisted the tug in retrieving fuel tanks, which had been carrying 1,800 litres of diesel and other debris, from the sunken vessel to minimise environmental damage.
It was the 53rd incident of the year for GAFIRS and the fifth incident in the last three days.
‘A huge thank you to everyone who assisted leading to a safe outcome,’ a GAFIRS spokesman said.