Watson was ruthless attacking the Czech world number 55's serve, time and again earning break points that Benesova had to dig deep to defend.
But Benesova's resistance seemed to be broken when she lost an epic game on her own serve while trailing 4-1 in the second set, with Watson going on to serve out for the match.
The only worry for Watson will be that she won just four of the 20 break points she earned in the match, which was moved on to centre court late in the day.
Watson was, as much as anything, relieved to have won the match against a player ranked 48 places above her in the world.
"I'm just so pleased to have got through that - it was tough not knowing when we would be on, and having to wait all day," she said.
"This is my first singles win at Wimbledon - including juniors," she said.
Britain could well have another woman in the second round with Johanna Konta locked in a tense battle with USA's Christina McHale when bad light forced play to be suspended.
World number 212 Konta - who switched nationalities from Australian to British just last month - took the opening set in a tie-break against world number 32 but lost the second set, and the players were tied at 7-6(4) 2-6 7-7 as the sun went down on SW19.
British men's number four Josh Goodall went out of Wimbledon at the first hurdle as he was beaten 6-4 3-6 7-6(3) 6-4 by Grega Zemlja.
Goodall, the world number 215, bounced back after losing the opening set to a man ranked 95 places above him, sparking hopes among the crowd that they could see a British winner.
But Slovenia's Zemlja, who like Goodall claimed a place in the tournament as a wildcard, took the third set in a one-sided tie-break, then finished off the match to set up a second round clash against Spain's Fernando Verdasco.
Eighteen-year-old Oliver Golding also went out in his opening match, but in far more heartbreaking fashion as he lost 1-6 7-6 7-6 7-5 to Igor Andreev.
Golding looked on course to shock Russia's Andreev, a former world number 18, as he took the opening set for the loss of just one game.
But the 28-year-old Andreev used all his experience against the world number 491 to take the next two sets on close-fought tie breaks before a late break in the fourth set to close out the match.
British women's number six Naomi Broady went out in straight sets, losing 6-4 7-6(4) to Spain's Lourdes Dominguez Lino.
World number 228 Broady earned four break points during the match but only converted one of them, with world number 71 Dominguez Lino holding her nerve better on the key points to end up the winner.