The Welsh beat Moldova 4-0 in their first qualifier, but drew against Austria, Georgia and Serbia.
Chris Coleman's side are third in Group D, four points behind the Republic, who are top.
"We've been unlucky where we've drawn a few games we felt we should have won," Burnley's Vokes told BBC Radio Wales.
The side finishing top qualify automatically, with eight of the nine second-placed teams facing play-offs to reach next year's World Cup in Russia.
Vokes added: "We've been apart for a few months, but if we can look back and take confidence from the last few performances, then I definitely think we can get the right result out there."
The 27-year-old knows they must win in Dublin to boost their chances of qualifying for a first World Cup since 1958. He says Real Madrid forward Gareth Bale and Arsenal midfielder Aaron Ramsey will provide welcome relief after struggling with injuries this season.
"It's good news for the team. They're two very important lads in our squad," he added.
"It's great to see they are back in training and fit and ready to go."
Burnley travel to the Liberty Stadium on Saturday hoping to seal a win that could send them into the top half of the Premier League table.
The Clarets lost against Swansea City at home on the opening day and Vokes is aware of the threat they pose given their recent return to form.
"We know that if we don't get the right result down there then it closes the gap for us [on the relegation zone]," Vokes said.
"It's important that we get the right results in the next few games to keep that distance between us and the bottom three."

The original film saw Tom Hanks play a man saved from drowning as a boy by a mermaid, whom he meets 20 years later.
Tatum - who will presumably be a merman - is set to co-star with Jillian Bell, according to Hollywood Reporter.
They starred in 2014's undercover cop comedy film 22 Jump Street, which topped the box office on its release.
The original film's director Ron Howard is set to produce the film, along with Tatum.
The film, a rom-com about whether the man will choose to remain on land or join the mermaid in the sea, was nominated for an Oscar for best original screenplay.
This version will be written by Maris Lewis-Ryan and follows on from Ghostbusters, which was remade this year with an all-female lead cast.
Tatum recently starred in Hail Caesar! with George Clooney and Josh Brolin, while Bell is to appear in Office Christmas Party later this year.

Samuel Armstrong, 23, of Copt Hill, Danbury, Essex, is charged with two counts of rape and one of sexual assault.
He has been suspended from his position as chief of staff to South Thanet's Tory MP Craig Mackinlay.
The charge follows an alleged incident at Parliament in October.
Mr Armstrong was bailed to appear before Southwark Crown Court on 28 April.
He was ordered not to enter the Palace of Westminster and not to contact the alleged victim.

The county council plans to prohibit buses, taxis and private hire vehicles from using Queen Street.
Oxford Bus Company said the authority needed to consider the "additional pressure" on surrounding streets.
The council said it was "vital" for more pedestrians and cyclists to use the route.
Oxford bus Company said: "We can't have a situation where Queen Street is pedestrianised but the additional pressure put on surrounding streets means that waiting conditions for bus passengers become unbearable, or walks between stops become unacceptably long - or our customers can't get taken to where they want to go.
"A credible, agreed plan therefore needs to be identified between all parties before Queen Street can be closed and dialogue is ongoing to achieve this."
Oxfordshire County Council said the street was one of the main routes across the city centre and added pedestrian and cycle numbers were expected to increase "significantly" in the future due to development across the city.
"It is vital that strong pedestrian and cycle links are maintained and encouraged, and improvements to the pedestrian experience are made, to ensure a well-connected and joined up city centre that will continue to thrive," it added.
A consultation on the proposals runs until 6 June.
Wales forward Sam Vokes hopes they can turn their World Cup qualifying fortunes around when they visit the Republic of Ireland on 24 March.
[NEXT_CONCEPT]
Magic Mike star Channing Tatum is to play the mermaid in a remake of 1984's film Splash, taking the role played by Darryl Hannah, according to reports.
[NEXT_CONCEPT]
An aide to a Kent Conservative MP has appeared before Westminster magistrates charged with rape following an alleged attack at the Houses of Parliament.
[NEXT_CONCEPT]
A "credible plan" needs to be agreed before any move to ban buses and taxis from a street in Oxford is made, a bus company has said.