The alarm was raised after the crew of the Gone Fishin vessel phoned for help off Barns Ness at 9.30am.
The pair from Penicuik had set out at 7am for a day’s fishing.
UK Coastguard ordered the inshore lifeboat to be launched, which reached the stricken boat at 10am.
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The volunteer crew of Alan Blair, Jamie Forrester, Andrzej Hajduk, Douglas Wight towed the fishing boat back into Dunbar.
They gave the anglers buoyancy aids to wear and reached harbour 40 minutes later.
The Royal National Lifeboat Institution said the engines of small motor boats should be regularly maintained.
It also advised they should also be equipped with lifejackets, a VHF radio and flares in case of emergency.
The incident happened two weeks after members of the Dunbar lifeboat crew came to the assistance of a colleague whose yacht had suffered engine failure.