Media playback is not supported on this device
David Healy's Blues came from behind to thrash Coleraine 5-1 while Stephen Baxter's long-time leaders fell to a 3-0 defeat away to Ballymena United.
As Linfield have a much better goal difference, a draw at Solitude would probably be enough to clinch the title.
Crusaders complete their campaign with a home match against Glenavon.
"Linfield are in a strong position now, but we will fight to the death and see what happens," said disappointed Crusaders manager Stephen Baxter.
"We knew it would be tough against Ballymena. They were up for the fight - David Jeffrey's teams always are."
When Linfield went a goal down at Coleraine, it looked like the Crues might be able to clinch the title with victory over Ballymena.
But after James McLaughlin's 50th-minute opener for the Bannsiders, Linfield hit back in style to run out clear winners.
Aaron Burns and Andrew Waterworth scored two each and Paul Smyth got the other.
"We always knew we would have to win all our matches and next Saturday is no different," said Linfield skipper Jamie Mulgrew.
"Cliftonville have beaten us twice this season already. For anyone to suggest it is a given for us to go there and win would be wrong and disrespectful to Cliftonville as a club.
"We must continue to perform at the level we have been doing."
Crusaders had a miserable afternoon at Ballymena, missing a number of chances before seeing Ballymena run out 3-0 winners.
Conor McCloskey blasted United into the lead on 71 minutes and Cathair Friel added the other two.
Ballymena's win takes them level on points with fourth-placed Cliftonville who lost 3-1 at home to Glenavon.
If Ballymena can seal fourth spot, it will be their highest league finish since 1981 when they were third.
Dungannon are destined to achieve a place in the play-offs by finishing seventh in the table.
Their 4-0 win over Carrick Rangers means the seventh-placed Swifts are three points ahead of Ards with a much better goal difference.
Linfield have knocked champions Crusaders off the top of the Irish Premiership and will clinch the title if they beat Cliftonville next week.