Konta, a semi-finalist last year, lost control of a match she seemed to have in her pocket and was mightily relieved to escape a sticky Court Two with victory, having squandered five match points in the second-set tiebreak.
With Andy Murray missing the tournament due to injury, Konta, seeded 22nd, and men's 21st seed Kyle Edmund are shouldering the hopes of the home nation.
Edmund enjoyed a routine 6-2 6-3 7-5 win over Australian Alex Bolt and is the last British man left standing after teenager Jay Clarke fell in five sets to Ernests Gulbis.
Konta seemed to be heading for a relatively comfortable win against tricky 21-year-old Vikhlyantseva.
She broke serve at 5-5 on her way to taking a tight opening set and had points for a double-break in the second set when Vikhlyantseva served at 2-4.
Konta failed to push home her advantage, however, and dropped serve in the next game when she fired a forehand over the baseline having battled back from 0-40 to 30-40.
Vikhlyantseva then held and Konta found herself in a difficult situation at 4-5 when she failed to punish a short ball and watched a backhand winner flash past her.
She saved the set point with a superb deep forehand after being pushed wide but a crass attempt at a dropshot handed Vikhlyantseva another chance to take the match into a decider.
Konta saved that one too but in the tiebreak she huffed and puffed as a 6-2 lead evaporated.
She double-faulted at 7-6 but held her nerve to knock off the next two points, finishing the match with an easy volley.
"First rounds are always tricky. The conditions were tricky, breezy and gusty, it didn't make it easy," Konta, who was beaten by Venus Williams in the semis last year, told reporters.
"I am playing this championships independent of what happened last year. I am a littler wiser this year, working hard to be here for a full two weeks."
Her next hurdle is experienced Slovakian Dominika Cibulkova while Edmund will play either Japan's Yuichi Sugita or American qualifier Bradley Klahn.
(Reporting by Martyn Herman; editing by Clare Fallon and Ed Osmond)
