However, several mechanical "hiccups" occurred that prevented the spacecraft from completing the maneuver and raised questions about the condition of the spacecraft's fuel system.
The team will attempt to refire the spacecraft's thrusters on Wednesday.
"The good news is the propulsion system works -- when it wants to," said Keith Cowing, a former NASA astrobiologist and a spokesman for the ISEE-3 Reboot Project.
The half-ton, drum-shaped satellite, which was retired by NASA in 1997, has been orbiting the sun since the 1980s.
As the probe neared Earth this year on a pre-arranged flyby, NASA gave permission to a group of former agency employees and engineers to take control of the 36-year-old spacecraft -- a historic first.
Operating in an old McDonald's restaurant at NASA's Ames Research Center in Mountain View, Calif., the reboot team initiated a sequence of "burns" just before 11 a.m. PDT.
"Command accepted ACCELERATION!!," the team announced on its Twitter feed.
The maneuver is an eleventh-hour attempt to wrest the probe from its sun-centric orbit. Each day that the probe nears Earth, it requires more fuel to change its flight path. By Aug. 1, the maneuver would require more than twice the amount of fuel available, according to the team's calculations.
The orbit change will require a total of 432 invidual pulses from the spacecraft's engines, and engineers have grouped those pulses into seven burn sessions.
"When you fire these little engines its like shooting out of a pea-shooter," Cowing said. "You have to do it a lot."
On Tuesday, ISEE-3 completed the first of its seven burn sessions without a hitch. When engineers commanded the satellite to begin its second session however, it quickly became clear there was a problem.
"We could tell the valves and things were working, but we did not see that the spacecraft was changing its trajectory or speed, which told us something was going on," Cowing said.
ISEE-3 is equipped with a dozen monopropellant hydrazine thrusters. Hydrazine, an extremely toxic substance, freezes at roughly the same temperature as water, so a series of heaters are used to liquefy the propellant before executing maneuvers.
The hydrazine is kept in eight fuel tanks, which also contain pressurized gas. When the spacecraft receives a command to open a fuel valve, the pressurized gas forces the hydrazine through a fuel line and into a catalyst.
The catalyst causes the hydrazine to break down, which produces a propulsive blast of hot gas. Unlike rockets taking off from Earth, the hydrazine blast is invisible to the human eye.
Before executing the first burn on Tuesday, the reboot team turned off the fuel line heaters to save power, raising the possibility that the fuel had become frozen and thus unable to come in contact with the catalyst.
"That's the first thing you think of," Cowing said. "But it could be something else. There may not be enough fuel for that to be an issue, or it's possible that the pressurant may have run out, or that there's a valve not doing its thing."
Like most spacecraft, ISEE-3's propellant system contains numerous redundant elements, and Cowing said he was confident that the team would determine the cause of the firing failure and figure out a work-around solution.
The window for ISEE-3's course alteration will remain open for several days.
"Ideally, we would have done it today, but if we do it in the next day or two or three, we're good to go," Cowing said.