The linkup occurred as the spacecraft zoomed more than 200 miles above the Atlantic and ended a round-the-world chase of nearly two days. The astronauts cheered when the hatches swung open, and the two crews greeted each other with hugs and handshakes.
A thruster failure made the rendezvous all the more challenging for shuttle commander Rick Sturckow.
One of Discovery's small thrusters began leaking shortly after Friday's midnight liftoff and was shut down. None of the little jets was available for the rendezvous and docking, and Sturckow had to use the bigger, more powerful primary thrusters, making for a somewhat bumpier, noisier ride.
Struckow had trained for this backup method - never before attempted for a space station docking - well before the flight. Mission Control congratulated him on "a fantastic job."
"You'll be happy to know it occurred on the 25th anniversary of the maiden flight of Discovery," Mission Control radioed.
Approaching from directly in front of the laboratory complex as both spacecraft sailed 220 miles above the central Atlantic Ocean at 5 miles per second, the shuttle's payload bay docking port engaged its counterpart on the front end of the statin's Harmony module at 8:54 p.m. EDT, about 10 minutes ahead of schedule, reports CBS News space analyst William Harwood.
Trailing the station by 9.2 miles, Sturckow and Ford fired the shuttle's left orbital maneuvering system rocket at 6:26 p.m. to begin the final phase of the rendezvous.
At 8:03 p.m., with the shuttle positioned about 600 feet directly below the station, Sturckow used the primary jets to kick off a slow nine-minute back-flip maneuver to expose the shuttle's belly to the space station.
"Station and Houston, from Discovery, capture confirmed," astronaut Patrick Forrester radioed from the shuttle.
The primary goals of the mission are to deliver 7.5 tons of science equipment, life support gear and supplies, including a treadmill named for Comedy Central's Stephen Colbert. The treadmill was launched in more than 100 pieces.
Nicole Stott, who hitched a ride to the station aboard Discovery, will replace astronaut Timothy Kopra, who plans to return to Earth aboard the shuttle in Stott's place after 57 days in space, Harwood reports.
But Stott won't have time to put the treadmill together until the shuttle is long gone.
Three spacewalks are planned, overnight Tuesday, Thursday and Saturday, to replace a 1,800-pound ammonia coolant system tank, to retrieve external experiments, deploy a spare parts mounting mechanism and to install wiring needed for a new module scheduled for launch next year.
Earlier in the day, Stott sent "big space hugs" down to her 7-year-old son, Roman, from Discovery. "I just want to let him know I love him more than anything," she radioed. Stott will remain at the space station until another shuttle comes to get her in November.
Space station astronaut Timothy Kopra - whom Stott was replacing - peered at his shuttle friends through a porthole in the hatch as he waited for the door to swing open. Kopra has been on board since mid-July.
"He's not looking for a ride home or anything, is he?" Mission Control asked.
"He looks like he's ready," Sturckow replied.
Discovery will spend more than a week at the orbiting complex. Astronauts will perform three spacewalks to replace an ammonia tank and perform other outside maintenance, with the first one on Tuesday night.
Monday evening's action will involve lifting the huge cargo carrier out of Discovery's payload bay, using a robot arm, and attaching it to the space station.
This is only the second time 13 people have been together in orbit. The first was just last month during Endeavour's space station visit.
Discovery, meanwhile, seems to have fared liftoff well.
The chairman of NASA's mission management team, LeRoy Cain, said Sunday that a preliminary look at launch pictures and other data indicates the shuttle had no major damage. No significant pieces of foam insulation were spotted coming off the fuel tank.
Cain cautioned that another few days of analyses are needed. Engineers got even more data after Discovery arrived at the space station. The shuttle performed a slow backflip on final approach so the space station crew could photograph its belly in a search for damage.