The event in Latvia is the first ranking event of the new season, and Carter opened with a break of 75 before Day responded with 88.
In the third frame a long red got Day in but he couldn’t capitalise, scoring just 15 before he allowed Carter back to the table.
Although Carter couldn’t completely clean up he did enough to win the frame and take a 2-1 lead.
Riga Masters
Robertson sets up Lisowki final in Riga
29/07/2018 AT 11:12
Carter missed a red for frame ball in the fourth thanks to some shenanigans with the spider, and Day took advantage when he came to the table to level up.
A couple of tense snooker battles followed and both players made errors, only for Carter to eventually triumph.
Carter will face Mark Allen in the next round after the Masters champion avoided a shock as he came from 2-0 down to beat Peter Lines 4-3, despite Lines making a break of 133
World champion Mark Williams got off to a brilliant start when he opened up a 3-0 lead over Ben Woollaston.
However Woollaston fought back to 3-2, including a century of 110, but Williams kept his cool to secure a 4-2 win.
Former world champion Neil Robertson lost the opening frame but recovered well to battle past Li Yuan 4-2 in his first round match.
WATCH THE RIGA MASTERS LIVE ON EUROSPORT AND THE EUROSPORT PLAYER
28-year-old Yuan took the opening frame but Robertson, 36, responded with breaks of 55 and 78 in the second frame to level things up.

'I'm just thankful I could repay her tonight' - Robertson's emotional tribute to wife

A break of 61 gave him the lead and another of 81 saw him pull back ahead after Yuan had levelled.
Robertson finished the match off with a break of 59 and that sets up a mouth-watering clash with Liang Wenbo in the next round after the 14th seed beat Kurt Maflin 4-2.
There was a shock as Barry Hawkins was knocked out by Li Hang, going down 4-3.
Hang got off to an electric start with breaks of 77 and 80, racing into a 3-0 lead before 'The Hawk' battled back to 3-3.
However he couldn't find the winner as he became the first real upset of the tournament.
And there was a second later on tour newcomer Ashley Carty shocked the experienced Anthony McGill 4-2.
Third seed Shaun Murphy missed out on a possible maximum when he missed a simple yellow on 120 but he still enjoyed a comfortable 4-0 win over David Lilley.
Joe Perry is through, beating Robert Milkins 4-3, as is last year's runner-up Stephen Maguire who beat Gerard Greene 4-1.
Ricky Walden wasted no time in seeing off qualifier Jimmy White, triumphing 4-0.

RIGA MASTERS ROUND ONE RESULTS

Mark Williams 4-2 Ben Woollaston
Oliver Lines 4-2 Alfie Burden
Mark Davis 4-2 Luca Brecel
Jack Lisowski 4-2 Ian Burns
Kyren Wilson 4-0 Luke Simmonds
Ashley Carty 4-2 Anthony McGill
Marco Fu 4-1 Xiao Guodong
Ali Carter 4-3 Ryan Day
Mark Allen 4-3 Peter Lines.
Li Hang 4-3 Barry Hawkins
Graeme Dott 4-3 Tian Pengfei
Ricky Walden 4-0 Jimmy White
Michael Holt 4-1 Liam Highfield
Neil Robertson 4-2 Li Yuan
Joe O'Connor 4-1 Lee Walker
Simon Bedford 4-0 Niu Zhuang
Joe Perry 4-3 Robert Milkins
Stephen Maguire 4-1 Gerard Greene
Michael White 4-3 David B Gilbert
Zhang Yong 4-0 Rory McLeod
Scott Donaldson 4-3 Robin Hull
Liang Wenbo 4-2 Kurt Maflin
Stuart Carrington 4-3 Fergal O'Brien
Craig Steadman 4-1 Zhou Yuelong
Lukas Kleckers 4-3 Robbie Williams
Joe Swail 4-2 Mei Xiwen
Shaun Murphy 4-0 David Lilley
Zhao Xintong 4-0 Nigel Bond
Jamie Jones 4-2 Rod Lawler
Mark King 4-2 Xu Si
Chris Wakelin w/o Sam Craigie
Riga Masters
Zhao Xintong dismisses Shaun Murphy in Riga
28/07/2018 AT 13:48
Riga Masters
Liang Wenbo denied 147 by lamentable run of the balls
28/07/2018 AT 11:16