Hank Aaron, the all-time leader with 755, now stands only 42 away.
Giants manager Felipe Alou said it was doubtful that Bonds would be in the starting lineup against Astros ace right-hander Roy Oswalt on Monday.
"After three straight games, I don't think you'll be seeing him [Monday] night," Alou said. "But I'm sure we'll be seeing a few more home runs on this coming homestand."
Bonds was noncommittal about playing.
"We'll have to see how I feel [Monday]," Bonds said. "It's a long flight."
Bonds hit homers 500, 600, 700 and 71-73 at the cozy park nestled on McCovey Cove, the latter three against the Dodgers in 2001 when he broke Mark McGwire's single-season record.
Now he has the opportunity to tie and pass the Great Bambino in San Francisco, where it always seemed meant to happen.
"We might as well keep tradition alive," Bonds said.
Just when a five-game road trip and an ugly three-game series against the Phillies seemed to be going down the drain, Bonds came to bat against the right-handed Lieber with two out and no one on in the sixth inning.
The homer was Bonds' fifth of the season, coming on a 2-1 sinker that was right out over the plate, Lieber said -- a titanic 450-foot blast that hit the glowing McDonald's advertisement on the facade of the third deck.
For the lefty swinger, it was also his first homer of the season to right field, the other four having been hit from the left-field line to dead center.
"He nearly knocked down that golden arches sign out there," said Phillies manager Charlie Manuel.
"I'm told that's the way the Babe hit them," Alou added. "Too bad he didn't get to play on this field."
It was Bonds' fourth home run of his career off Lieber, who is among the 419 pitchers to allow at least one homer to Bonds in his career. It was also his second at the Phillies' new ballpark. Previously, he had hit 27 at the now-demolished Vet. It was No. 62 against the Phillies, tying his total against the Dodgers for third most against any Major League team.
Bonds has hit 63 against the Expos/Nationals and 82 against the Padres.
Coming into the fateful at-bat against Lieber, who intentionally walked him to loud jeers in the first inning, Bonds had been 2-for-11 since he hit No. 712 this past Tuesday off San Diego's Scott Linebrink in his last at-bat of the Giants' 5-3 loss.
In his first at-bat with a chance to tie Ruth during the eighth inning, Bonds whiffed against lefty reliever Aaron Fultz for the second time in the series. Bonds fouled back the first pitch, scaring the Bambino out of Fultz.
"He just missed it," Fultz said. "A quarter of an inch either way [on the ball], it goes farther than the one he hit off Lieber."
During the past few weeks, Bonds has declined to speak about the specter of Ruth, although he finally started addressing the issue during a postgame press conference on Sunday night.
"Babe Ruth was a great, great baseball player," Bonds said. "Ruth started all this. He was in a league of his own. He brought the game to a different level and brought people into the stadium. All of us look up to Babe Ruth and Hank Aaron and the guys before us."
Asked if he would consider himself a better player than Ruth once he passes him, Bonds added: "I don't know yet. But the numbers speak for themselves."