The 24-year-old saw a deadline-day move to Liverpool collapse with Spurs also linked along the way, though coach Tim Sherwood has always distanced the club from a deal.
Konoplyanka himself said he does not see the round-of-32 tie as an audition for a summer transfer but he was lively throughout and gave full-back Kyle Naughton an unsettled evening.
The penalty was awarded with just 10 minutes remaining after referee Antonio Miguel Lahoz had turned down several claims from both sides throughout the game.
Konoplyanka stepped up and scored with the air of a player with the confidence to move on to bigger and better things, but for now he has given Dnipro and former Spurs boss Juande Ramos a lead to defend at White Hart Lane next week.
It could have been a different story had Roberto Soldado not missed in spectacular style earlier in the second half.
Spurs boasted a 100 per cent record in getting out of their group under previous head coach Andre Villas-Boas but, with Sherwood taking charge of his first European game, it was a second-half sitter turned over the crossbar by summer signing Soldado which he will be left pondering.
Dnipro supporters sang the Ukrainian national anthem during the minute's silence before kick-off, with black armbands also worn by both teams to honour those who have lost their lives during the political protests in capital Kiev in recent weeks.
With a national day of mourning also declared for Thursday, many fans stayed away from the Dnipro Arena but those who did make the journey were richly rewarded.
Tottenham's first effort on goal came courtesy of a wayward volley from the boot of Paulinho, who was pushing forward to support lone frontman Soldado as much as possible.
The Brazil international was then guilty of losing possession and allowing the hosts to break, with Konoplyanka ghosting past Naughton before seeing his cross poked wide by Matheus.
Soldado had the best chance of the early exchanges as he glanced Nacer Chadli's cross towards goal, with Dnipro goalkeeper Denys Boyko equal to the header.
Brad Friedel, deputising in goal with Hugo Lloris not on the trip, was almost caught out moments later as he rushed from his line to clear only to find Dnipro skipper Ruslan Rotan, who could not lob the American as he made his way back to goal.
Dnipro wasted the best opportunity of the first half as Matheus raced through behind the Tottenham backline and, after not being adjudged offside, spurned the chance to put the hosts in front as he dallied before shooting straight at Friedel.
Rotan forced a better save from Friedel shortly afterwards as he arrowed in a low effort which the 42-year-old pushed straight into the path of Roman Zozulya, who lost his footing at the crucial moment.
With the game now at a more frenetic pace, Spurs also created a great chance as Danny Rose's cross fell to Chadli but the winger could not control his dipping drive.
Matheus skipped past a combination of Rose and Etienne Capoue before tumbling in the area, with referee Lahoz not buying the dive but opting against booking the Brazilian.
He did award a free-kick right on the edge of the Dnipro area when Matheus' compatriot Paulinho was felled by Ivan Strinic, with Townsend's dipping set-piece flying just wide.
Referee Lahoz was involved again on 55 minutes as he deemed Zozulya had dived under pressure from Friedel following a fierce free-kick into the Tottenham box.
Soldado, who has struggled to live up to his billing since his summer move from Valencia, missed the visitors' best chance when he spooned Paulinho's cross over from five yards out.
Sherwood introduced Christian Eriksen from the bench shortly after the hour and the Denmark international thought he had made an immediate impact as he finished well only to see an offside flag raised on the far side.
Friedel kept the tie level as he did well to keep out Matheus' drive before Nabil Bentaleb became the next player to fall theatrically inside the box with Lahoz again unmoved.
Much like the first half, the game had burst into life following a scrappy spell and Soldado was unlucky to see a sweetly-hit volley deflect behind for a corner.
Ondrej Mazuch headed over a corner with 17 minutes to go before the game turned on a penalty decision as Lahoz was finally persuaded into pointing to the spot for the hosts.
Jan Vertonghen brought down Matheus and Konoplyanka made no mistake with the penalty as his effort went in off the post.
Substitute Harry Kane could not turn home a couple of good chances before Friedel saved well from a deflected Konoplyanka free-kick.
Zozulya then hit the post as Dnipro looked to further their lead, but they had to settle for just a one-goal advantage to take to England.
Source : PA
Source: PA