The boat, which first came into service in 1938 but was converted into a pleasure vessel after being replaced in 1976, was first on the scene after spotting flares coming from a 15ft craft at the Whitby Harbour entrance at 1.15pm.
The Mary Ann Hepworth reported the incident and stayed close to the stricken boat while the Humber Coastguard helicopter and current Whitby all-weather rescue vessel and in-shore lifeboat raced to the scene.
The two men on board, from Northallerton and Thirsk, were rescued and the boat was towed back to shore.
Mike Puplett, watch manager at Humber Coastguard, told the Yorkshire Post: “It was one last rescue for the Mary Ann Hepworth, she returned to the old days and performed admirably.
“It was lucky this was not any worse.
“The people on board did the right thing by firing off the flares.
“They were in a sticky situation but it was quickly resolved.”
The vessel ran into difficulties when its main engine failed, then water coming on to the boat flooded its smaller engine.
The Mary Ann Hepworth has one of the longest records of service in the Royal National Lifeboat Institution fleet.
She came into service on April 11, 1938, having cost £6,576 which was donated by Mr W Hepworth of Hull.
The 41ft Watson class boat was fitted with two 35hp petrol engines and sails and was considered state-of-the-art for her time.
In 1974, after serving 36 years, being launched 372 times and saving 201 lives, she was replaced by the Waveney class lifeboat, The White Rose of Yorkshire.
In 1988, Barry Snedden who was a crewman on the Whitby lifeboat bought her and returned her to the town to be used as a pleasure boat.