I think you need to scootch your definition of a “successful” Baroque composer down a little bit! I’d consider both Bach and Vivaldi very successful. They made a comfortable amount of money and were known and respected for their musical work among people who cared about such things (though both somewhat as virtuosos more than composers I suppose, but that was typical), and I mean, what else can you ask for out of a musical career, especially in that time period? If you could get someone to regularly pay you to compose music, you were a winner baby. Composing music was seen as more utilitarian work than it is today. Music was a product, a luxury product sure, but a consumable product (people did not like to reuse music as much as we do now for Art Music), made by people the nobility considered a servant. Music was thought of much closer to a craft than an art. Might be comparable to today’s video game workers’ status not as “artists.” Would you consider the people who did the 3D models for Wind Waker artists or technicians?

Have you ever heard of the “back door” measure of music’s status? So back in ye olden days, when a musician visited a house to give a performance, he or she would have been kept carefully separate from the guests, used the back door (like a servant) and not the front door (like a guest) and in very strict households, eaten with the servants as well. Some houses even had little velvet ropes to cordon off musicians while they were working. The “back door” status faded away in the mid 19th century, as the status of music makers rose. Composers, also, wouldn’t have even had the highest status inside the circle of music workers, that would have been reserved for star singers. This old post of mine seems an unrelated question, but it’s actually not, and gives a good run-down of how a composer would have been seen through this period.

Though I totally agree with /u/euozof, the real answer is “Handel, specifically when he rebirthed himself without the umlaut.” Though even he had his struggles and things people considered to be flops. You should also look at Nicola Porpora, J.A. Hasse, and Niccolo Jommelli as some other successful composers of that period that you probably haven’t heard of now. Pergolesi, also, is an interesting example of someone who gained fame very shortly after they died, in the same period they composed in, you might look into his life.