Jimmy Connors advanced easily to the third round of the French Open tennis championships today with a 6-1, 6-1, 6-4 victory over teen-ager Ramesh Krishnan on the red-clay center court at Stade Roland Garros.

Connors, playing in the world's premier clay-court tournament for the first time since 1973, had to wait through two long rain delays before getting on the damp, heavy clay. But once he did, he made short work of the son of former Indian Davis Cup player Ramanathan Krishnan, renowned as one of the game's great touch players.

The first of the tournament's seed players to fall was Jose-Luis Clerc, No. 11, who succumbed to young Gilles Moretton, 6-4, 6-2, 6-3.

Clerc, a rising star of 22, had overcome a 101-degree fever to beat Dick Stockton in five sets in the first round, but his continuing battle with flu left him listless for today's match.

Vitas Gerulaitis, who won the Italian Open last weekend, breezed past Brad Rowe, 6-4, 6-1, 6-2. Gerulaitis is seeded fourth behind defending champion Bjorn Borg, Connors and 1977 champ Guillermo Vilas. Borg and Vilas were idle today.

Chris Evert, the champion of 1974-75 and No. 1 seed in women's singles, defeated Laura DuPoint, 6-3, 6-2, in the last match of the rain-abbreviated program completed on the stadium court.

Her husband, British Davis Cup player John Lloyd, who has won only one of 17 matches in the last seven months, was trounced by lightly regarded Dominique Bedel, -2, 6-1, 6-4.