Giants 8, Cubs 6 (10). San Francisco started Bud Black, who was on his way to leading the NL in losses in 1991, but who was a generally solid pitcher; he would post a winning record and above-average ERA in his 15-year career, and won a World Series with the 1985 Royals. He would go on to be an apparently decent manager for the Padres for parts of nine seasons before being fired last year.
In fact, to this point in their respective careers, Black had earned over three times as many WAR as his Chicago opponent. But since said foe was the young Greg Maddux, Black's advantage would be short-lived.
Maddux allowed a two-out single to Mark Leonard in the top of the first, but left him on; Black yielded hits to Ryne Sandberg and George Bell in the bottom of the inning, and stranded both of them. With two outs in the second, Greg Litton singled, Jose Uribe walked, and Maddux wild pitched them to second and third, but Black was up next and struck out to end the threat; Luis Salazar then led off the bottom of the inning with a homer, putting the Cubs in front 1-0.
The Giants responded in the top of the third. With one out, Willie McGee singled and stole second, then came home with the tying run on Leonard's single. One out later, Kevin Bass reached on an Andre Dawson error, Terry Kennedy walked to load the bases, and Litton doubled to put the Giants in front 3-1. Uribe was intentionally walked, and for the second straight inning Maddux retired Black to leave two runners in scoring position.
San Francisco extended its lead in each of the next two innings. Leonard doubled and Matt Williams singled him home in the top of the fourth. In the fifth, Litton singled, moved to second on a groundout, and scored when Black reached on a Sandberg error. Tony Perezchica's double moved Black to third and chased Maddux in favor of Les Lancaster, who brought the inning to a close with the Cubs now trailing 5-1.
Black had allowed only a single to Sandberg in his previous two innings, and continued his effectiveness in the fifth, working around a hit by Jerome Walton. Paul Assenmacher struck out the side in the top of the sixth, and in the bottom of the inning, Chicago began closing its deficit. Dawson singled with two outs, which seemed rather harmless when Salazar fell behind 1-2 - but Salazar and Hector Villanueva proceeded to homer on back-to-back pitches, pulling the Cubs within 5-4.
(This is almost certainly not the unlikeliest set of back-to-back homers in baseball history; Villanueva did not have a terribly distinguished career, amassing only 516 plate appearances in four years of backup catching, but he hit 25 homers in that time. Salazar, meanwhile, played much longer, exceeding 4000 PA, and hit 94 homers. Still, though, it's not a terribly likely pairing. Based on their career home run rates, the odds of back-to-back homers from this pair would be about 1 in 960 - which means that if they had hit consecutively for every plate appearance of Villanueva's career, the odds would barely have favored this happening once.)
Assenmacher was flawless again in the seventh, and Chicago completed its comeback in the bottom of the inning. With one out, Walton and Sandberg walked. Mark Grace then singled, scoring Walton with the tying run and chasing Black from the mound. John Burkett assumed pitching duties against Bell, who hit into an unknown fielder's choice; the unknown fielder most likely threw home, attempting to cut off the go-ahead run, but Sandberg beat the throw home, and the remaining runners were safe as well. Burkett attempted to pick Grace off of second and threw errantly, albeit not to such an extent that the runners advanced; Dawson followed with a single to load the bases and bring Salazar to the plate, but the so-far hero proved mortal this time around, hitting into an inning-ending double play.
Heathcliff Slocumb took the mound in the top of the eighth and worked around a Perezchica single; Kelly Downs allowed a hit to Shawon Dunston and walked Joze Vizcaino in the bottom of the eighth, but left them both on. Dave Smith relieved in the ninth to try for the save; his attempt lasted until his fifth pitch, which Williams hammered for a game-tying home run. Bass followed with a single, but was doubled off on a Kennedy line drive; Downs then retired the Cubs in order to send the game to extras.
Smith remained on the mound in the tenth, and it went even less well than his previous inning. Uribe led off with a walk, and Mike Felder was then hit by a pitch. The next two hitters were retired, with McGee's flyout moving Uribe to third. Felder then stole second with pinch hitter Mike Kingery at the plate, and on the next pitch, a passed ball brought Uribe home with the go-ahead run. Kingery followed with a single that plated Felder, though Kingery was thrown out trying for second. Dave Righetti proceeded to set the Cubs down in order, ending the game.
The Cubs got two homers from Luis Salazar and one from Hector Villanueva in this game, and they had Greg Maddux on the mound. Even though Maddux didn't produce his best work, they still turned a lead over to their closer in the ninth, a man who entered 1991 having posted 7 consecutive ERAs below 3.
And they still lost. I believe the general term for a game of this type is "one that got away."