Okay so in the end Cooper can only send the message to Murph because of the technology of the Tesseract, but the technology is only obtained by his message, so it's a chicken or the egg sort of paradox as to what came first. So there were two timelines. What we see in the movie are the events that happen in the second timeline. The first timeline takes place off screen.
First Timeline:
Much of what happens in the second timeline also happens in the first timeline. The wormhole opens. Mann, Brand and Cooper work on the Lazarus Project. Just as it happened in the second timeline, Brand and Cooper are in the same position after visiting Mann's ice planet, and so Cooper sacrifices himself in Gargantua so that Brand can escape to the desert planet to start the colony. Brand ins utes Plan B on the desert world. Those people go on to evolve into Humanity's future, with a stable Black Hole to guide their sciences. They evolve to work in the 5th dimension, and decide they want to save their ancestors. THEY find Cooper in Gargantua and create the Tesseract for him. Remember at the beginning of the movie where Cooper is dreaming about his doomed training mission that caused him to leave NASA? Well in the first timeline he never crashes. He never leaves NASA, thus he never gets married and starts a family. He goes on the Lazarus Project without any familial attachments. They initiate their original gravity burst to down Cooper's training flight for the original Lazarus mission. This leads Cooper to leave the program, marry someone, and have children. This change creates a second timeline, and creates Murph, key to their plan.
Second Timeline:
This is what we see in the movie. THEY cannot interact with Murph, because she did not exist in their original timeline, so they use Cooper in the Tesseract to communicate with her, via love and gravity. His purpose here is two-fold: to guide himself back to Lazarus after THEY diverted him and to bring Murph into Lazarus, to fulfill the promise of Brand's Plan A. The message with the coordinates leading to the secret NASA facility leads to Cooper rejoining Lazarus just as before and in the process it realigns his second timeline with his first. Once in the Tesseract again (or the same original time due to 5th dimension mechanics) he relays the TARS data to Murph and she makes Plan A a reality. Cooper Station lifts off as a sort of galactic Noah's Ark, and begins it's slow trek towards the Wormhole.
Cooper is released from the Tesseract, and recovered on Cooper Station just outside Saturn for a final reunion with Murph before she dies. He then leaves in a ship to rejoin Brand on the desert planet, knowing that because of time dilation not nearly as much time has passed for her locally. Cooper and Brand create the second age of Humanity, those that will become THEY as they wait for the survivors of Earth to reach them in their slow gravity ship that is Cooper Station.