But it fell a bit short.
The Rangers scored only two runs despite putting six runners on base in the first two innings. They grounded into an inning-ending double play with the bases loaded in the first and hit two flyouts with runners on second and third and one out in the second.
Things spiraled quickly after that.
"He's a good pitcher, and when you have a guy like that on the ropes, you have to try to put him away," Rangers manager Ron Washington said of Lincecum after his club's loss. "But you don't always put those kind of guys away."
Texas came out of the gate hot. Elvis Andrus singled, Michael Young drew a walk, Josh Hamilton's groundout to the right side moved both runners up and Vladimir Guerrero hit a hard comebacker off Lincecum to give his club a 1-0 lead in the first.
Then, the Rangers loaded the bases when Lincecum fielded a comebacker and caught Michael Young between third and home but never made a throw. Lincecum said he pretty much thought two baserunners were going to end up at third base on the play.
"That was a little bit of a brain fart there, not really knowing the situation," Lincecum said. "Obviously, those aren't the kind of situations you want to be in."
Not to worry, Lincecum escaped the threat on the next batter, when he got Ian Kinsler to ground into a 5-3 double play with a first-pitch slider. Heading into that at-bat, Kinsler was 3-for-9 with five RBIs with runners in scoring position in this postseason.
"Yeah, we missed some opportunities, but that's the way baseball is played sometimes," Kinsler said. "You don't capitalize on every single opportunity that's presented to you. It would be nice if you did, but tonight we didn't."
The Rangers still got to Lincecum in the second, when Bengie Molina hit a leadoff single and, two batters later, Lee roped a double in the left-center-field gap to become the first American League pitcher to notch an extra-base hit in the World Series since Chad Ogea in 1997.
But Andrus brought in only one run with a sacrifice fly to center field, and Young couldn't capitalize with two outs.
After that, Lincecum retired 11 of the next 12 hitters he faced.
"You're going to have opportunities, and if you don't take it, they're going to take it," Andrus said. "That's the way it is."
And that's exactly what happened.
The Giants wound up scoring 11 runs the rest of the way -- two in the third, six in the fifth and three in the eighth -- and notched a Game 1 victory after surviving a desperate ninth-inning rally by Texas.
The Rangers were 4-for-12 with runners in scoring position and left eight runners on base. The Giants? They had as many hits (nine) with runners in scoring position as they had during the entire National League Championship Series, and six of their 11 runs came with two outs.
"They did what we didn't do," Texas left fielder Nelson Cruz said. "They scored when they needed to."
Could things have gone differently if the Rangers had taken full advantage of those run-scoring opportunities that were slightly open in the first couple of frames?
"Maybe," Young said. "But [Lincecum] made a couple of pitches when he had to, and you have to give him credit for that. So we'll refocus for tomorrow and get ready to play."