Eighth-seeded Dimitrov, 19, earned his victory since the Australian Open with a 6-0, 6-2 rout of former world No. 5 Rainer Schuettler, who managed to win only one service game during the 63-minute match.
Meanwhile, seventh-seeded Cuevas also encountered little difficulty in a 6-2, 6-0 win over Brazil's Ricardo Mello in 53 minutes on the green clay at River Oaks Country Club.
Also Monday, Igor Andreev downed American Michael Russell, 6-2, 6-3.
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