Gylfi Sigurdsson has warned Hull his Swansea side will give them no margin for error as the sides go toe to toe in the Premier League relegation battle.
With Sunderland down and Middlesbrough hanging by a thread, the final place in the bottom three looks likely to be settled in a straight scrap between Swans and Tigers.
Both teams have been revitalised by managerial changes, Paul Clement bringing stability and organisation to the Liberty Stadium and Marco Silva overhauling things dramatically in East Yorkshire.
But one of them is destined to fail and Sigurdsson - whose brilliant equalising free-kick against Manchester United kept Hull's lead at two points - expects it to go all the way to the final round of fixtures.
" We're a point closer now to hope," he said after an encouraging afternoon at Old Trafford.
"It doesn't give Hull too much breathing space and they can't afford to slip up too many times now. It w as important for us not to be going away with nothing.
"We're getting to the end of the season where teams are fighting for their lives and they are going to get results. We're focusing on ourselves and putting the pressure on them so we don't give them any chances to escape.
"I think it is going to go all the way to the last game. They probably didn't expect us to get anything from the game today. It's good for us to cancel out the point they got."
Swansea might have woken up on Bank Holiday Monday out of the bottom three had striker Fernando Llorente made a decent connection with a glorious late chance.
The Spaniard appeared to freeze as he met a cross he could have headed or volleyed and the chance went begging, but Sigurdsson was in phlegmatic mood.
"Shoulda, woulda, coulda," he said. "He's scored a few important goals for us. You don't score them all, so as long as he's in the right position to get on the end of them I'm sure he'll score the next one."
Swansea might also have been in line for three points had England striker Marcus Rashford not won a soft penalty to give United the lead.
Clement insisted referee Neil Swarbrick had been "deceived" and goalkeeper Lukasz Fabianski was left "furious" by the decision.
But Sigurdsson insists there is no time for wallowing in injustice ahead of their critical run-in against Everton, Sunderland and West Brom.
"We can't be blaming someone else or the officials. We should have made sure we got our points earlier than coming into the last three games," he said.
"It's totally down to us that we're in this position, it's not down to decisions here or in the next few games. We've got to look at ourselves and put it right.
"If you'd asked me to put money on it (the penalty decision), if I was 100% sure, I wasn't. It didn't look like he touched him too much but it's difficult for the refs because they don't have the chance of a replay."