Harkleroad, 22, came from 4-1 down in a second set littered with unforced errors to give the hosts an unbeatable 3-1 lead at La Jolla Beach & Tennis Club.
Lindsay Davenport and Lisa Raymond wrapped up the tie 4-1 by outplaying Tatjana Malek and Anna-Lena Groenefeld 6-2, 6-0 in the dead doubles rubber.
The US advanced to an away semi-final on April 26-27 against defending champions Russia.
Earlier on Monday, Davenport swept aside Germany’s Julia Goerges 6-1, 6-2 in the first reverse singles match after the teams began the day locked at 1-1.
Harkleroad, who capped a memorable debut in the team competition with successive singles victories, traded early breaks of serve with Lisicki.
A tight opening set then went with serve until the ninth game when the German was broken after netting a forehand.
Leading 5-4, world No 74 Harkleroad held off a spirited display by Lisicki in a protracted 10th game before converting a third set point when her opponent hit a forehand long.
Lisicki, ranked 129th, took early control of the second set, breaking the American and forging 4-1 ahead.
The Fed Cup rookies exchanged breaks of serve in the seventh and eighth games before Harkleroad tightened her grip.
She broke Lisicki in the ninth with a rasping forehand winner, held in the 10th, broke again in the 11th and clinched victory when the German netted a backhand service return.
“I’m just proud of myself and super excited at the way that I played and handled my nerves at the end,” a beaming Harkleroad told reporters after completing a victory lap around the court with a US flag raised in one hand.
“I felt like my arm weighed a hundred pounds. I was a little bit nervous but I always had a plan today.”
Davenport, 31, got the home team back on track by outclassing Fed Cup debutant Goerges.
The American former world No 1, who suffered a shock defeat in Saturday’s opening singles encounters, broke the German twice in the opening set to take control.
The 19-year-old German, struggling with her serve, was again broken in the first, third and fifth games of the second before Davenport surprisingly lost the sixth when serving for the match.
Goerges held serve before Davenport, ranked 44th after returning to the court last September following an 11-month absence to have a baby, powered down two aces to wrap up a one-sided win.
“I played better today although I still have some ways to go,” a smiling Davenport said. “Most importantly I got a victory to put the team up.
“It was great to see Ashley do so well. In some ways, it makes the win even more exciting. She really carried the team and played great.”
But Harkleroad could be dropped for the next round because the semi-final tie almost certainly be played on a slow clay surface in Moscow, and accept they have to field their strongest team to have any chance of progressing.
If available, their best singles players would come from the Williams sisters, Serena and Venus, and Davenport.
“It all depends who we get to field,” Davenport told reporters after winning her last two rubbers on Monday in the first-round tie against Germany.
“If we can field our strongest team, we have a great shot (against Russia). If not, it’s going to be tricky because it’s going to be, I’m sure, on a slow red clay court which is obviously not the Americans’ best surface.
“We are fired up. We’re going to try and talk either Venus or Serena into coming.”
Neither of the Williams sisters was available for the La Jolla tie, although Venus did consider playing in it.
“Venus had me wait probably till a week up until (the team was announced),” US Fed Cup captain Zina Garrison said. “She was going back and forth. She basically said she played five weeks straight and couldn’t do it. Look for her in April.”Harkleroad said she would not be disappointed if overlooked.
“It just means that I would be able to continue to play tournaments and work on my own ranking, continue to play and continue to move up,” added the 22-year-old, who crushed Tatjana Malek 6-1, 6-3 in Saturday’s opening singles.
“So I wouldn’t be disappointed. They (Russia) are a tough team. But I definitely would be all for it if they asked me to go to Moscow, for sure.”
Results:
United States beat Germany 4-1
Played on Monday:
Lindsay Davenport/Lisa Raymond (US) bt Tatjana Malek/Anna-Lena Groenefeld (Germany) 6-2, 6-0; Ashley Harkleroad (US) bt Sabine Lisicki (Germany) 6-4, 7-5; Davenport bt Julia Goerges (Germany) 6-1 6-2.
Played on Saturday: Lisicki bt Davenport 6-1, 7-5; Harkleroad bt Malek 6-1 6-3.—Reuters