A huge slice of fortune kept Liverpool in the hunt for Champions League qualification on Monday, while second-tier Reading reached its first FA Cup semifinal since 1927 by ending Bradford's surprise run in the competition.

Jordan Henderson scored a fluke goal in the 68th minute to earn Liverpool a 1-0 victory over Swansea in the Premier League, with a covering clearance slamming into the right shin of the England midfielder and looping over the goalkeeper from the edge of the box.

"I got a little bit fortunate with the finish," Henderson said, "but you have to be in the right position to score."

Liverpool extended its unbeaten run in the league to 13 games — stretching back to Dec. 14 — and stayed only two points behind fourth-place Manchester United, which occupies the final Champions League qualifying spot. The two fierce rivals meet at Anfield on Sunday.

Third-tier Bradford had already beaten Premier League sides Chelsea and Sunderland en route to the FA Cup quarterfinals, but came unstuck at Reading in a 3-0 loss.

Reading scored twice in the opening nine minutes, through Hal Robson-Kanu and Garath McCleary, and Jamie Mackie added a third in the 68th minute after Bradford midfielder Filipe Morais was sent off for a dangerous challenge.

The match was marred by allegations of racial abuse from a fan toward McCleary, as the Jamaica international went to collect the ball for a corner. Reading said in a statement that the matter was passed onto a police after it was reported to match officials, and that "a man was then arrested and ejected during the halftime interval."

Reading, which is in mid-table in the League Championship and managed by former Chelsea assistant coach Steve Clarke, will play titleholder Arsenal in the semifinals at Wembley Stadium on April 18 or 19. It will be the first time Reading has played a top-division team in this season's competition.

The other semifinal sees Aston Villa facing either Liverpool or Blackburn, who will play a replay after drawing their quarterfinal 0-0 at Anfield last weekend.

That was the only time Liverpool has failed to win domestically since the start of February and the Reds struggled for attacking inspiration in the first half against Swansea, too. Goalkeeper Simon Mignolet kept Liverpool level with two stunning saves, from Bafetimbi Gomis and Gylfi Sigurdsson.

Some tactical tinkering in midfield for the second half proved key, though, and an improved display after the break was capped by a Henderson's lucky winner — the third league game in a row that he has scored.

He raced onto a neat flick by Daniel Sturridge but was beaten to the ball by Swansea defender Jordi Amat, whose sliding clearance hit Henderson. The ball skimmed off the wet surface and ballooned over the stranded Lukasz Fabianski.

Sturridge hit the post in second-half injury time for Liverpool, which kept a sixth straight clean sheet away from home.

"We are high on confidence and have great momentum," said Henderson, whose team trimmed the gap to second-place Manchester City to four points.