The Frenchman, who has had a disappointing season and is in danger of finishing outside the top 20 for the first time in six years, now faces 16th-seeded American Robby Ginepri in the two million-euro ($2.41 million) hardcourt tournament.
The partisan home crowd on centre court had something to cheer, however, when Fernando Verdasco overcame a second set wobble to beat France's Paul-Henri Mathieu 6-4, 3-6, 6-3.
Another Spaniard Alberto Martin fought back from a set down to earn a 3-6, 7-6, 6-4 win over Jiri Novak of Czech Republic who was a finalist here in the 2002 inaugural edition.
Argentines Agustin Calleri and Juan Ignacio Chela, who both had to qualify, breezed through their matches. Calleri disposed of Spain's Albert Costa 6-0, 7-5 while Chela beat 2003 finalist Nicolas Massu of Chile 6-2, 6-3.
Eleventh seed David Ferrer of Spain will be Calleri's next opponent, while Chela now meets Sweden's Thomas Johansson.
Austria's Juergen Melzer, who beat American Vince Spadea 3-6, 6-4, 6-3, was rewarded with a tough second-round match against fifth seed David Nalbandian.
Victor Hanescu of Romania overcame Czech Tomas Zib 6-1, 6-4 to earn a clash with top seed and world number two Rafael Nadal on Wednesday.
Spain's world number two Rafael Nadal withdrew from last week's tournament in Vienna because of a knee problem but confirmed he would play in Madrid after further tests on Monday.
Britain's Tim Henman faces American Taylor Dent in Monday's late match.
Grosjean and Lopez began in confident mood as they delivered a succession of high-speed serves on centre court.
But Grosjean, who lost to Andy Roddick in the final of the U.S. clay court event in Houston this year, stepped up a gear on the Lopez serve to earn three set points at 6-5.
LOOSE SMASH
The Spaniard then fired a loose smash to gift his opponent the first set.
The 24-year-old Lopez broke in the third game of the second set and served out to level the match.
He put Grosjean's serve under pressure at the start of the deciding set but cracked in the fourth game, surrendering his serve to trail 3-1.
Grosjean broke again in the eighth game to secure victory.
Calleri caught Costa cold, breaking serve in the opening game before reeling off the next four to lead 5-0.
The Argentine, who reached the final in Amersfoort in July, went 40-0 up in the sixth game and took the set at the first opportunity after a ragged-looking Costa punched a second service return into the net.
The 30-year-old Spaniard put up more of a fight in the second set, winning the first game and going on to take a 5-4 lead, but Calleri broke in the 12th game before serving out for the match.
Costa said he would contemplate retirement during the close season.
"I'm going to leave the door open at the moment and will take a month off and then see if I recover the strength and motivation to carry on, if not it won't be worth it," he said.
More from rediff