The team, of which Wright is vice-skip, defeated the Latvians 9-5 on Wednesday in the Olympic Qualification Event in the Netherlands.
It was enough to guarantee the European champions a place in the play-offs of the tournament which will determine which countries fill the three remaining slots available for February’s Winter Games in China.
Team Muirhead got off to a shaky start in Leeuwarden, losing to Turkey and Korea after winning their opening match against the Czech Republic.
But wins over Japan, Germany, Estonia and now Latvia have put them back on track.
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Skip Muirhead said: “We’re delighted to get into the playoffs.
"That was our number one goal coming here, to get that top four spot and we’ve done that.”