Top-flight Wigan Athletic needed a penalty shootout to eliminate second division Leeds United, who came from behind four times over the two matches and forced a 3-3 draw after extra-time in the replay.
Second division Stoke City also needed penalties to see off minor league Tamworth after their replay finished 1-1 while Premier League Birmingham City ran out 2-0 winners over fourth division Torquay United.
Middlesbrough, savaged 7-0 by Arsenal in the league at the weekend, took out their frustrations on Nuneaton Borough with a 5-2 victory over the minor league club.
Reading, so keen to secure Premier League status they rested several regular starters, trailed 2-0 after a first-half double from West Brom’s Richard Chaplow.
Lita got one back for the home side after the break and added a second with a beautiful strike a quarter of an hour later to send the match into extra-time.
The 21-year-old then finished off a good move to claim his third goal.
Reading now play Birmingham, who had Jiri Jarosik and Mikael Forssell to thank for their 2-0 triumph over Torquay.
At Elland Road, Wigan’s Swedish striker Andreas Johansson put the visitors into a deserved lead in the 24th minute.
Leeds equalised four minutes from the break when Lleyton Baines cleared a Rob Hulse header off the line and David Healy was on hand to score.
Jason Roberts turned and lashed home Wigan’s second five minutes into the second half but Leeds levelled again when Healy converted a 64th-minute penalty.
Twelve minutes into extra time, Roberts rose to nod in a Graham Kavanagh cross but a screamer of a shot from Ireland fullback Gary Kelly sent the tie into the penalty shootout.
Misses by Healy and Hulse left Kavanagh needing to convert his spot kick to clinch victory and the Irishman delivered a 4-2 win on penalties, setting up a fourth-round tie against Manchester City.
Nathan Jackson put Tamworth in front against Stoke but Paul Gallagher saved his side’s blushes by equalising 10 minutes from time.
After a scoreless extra half-hour, Stoke prevailed 5-4 in the shootout and next play Walsall, who beat fellow third division side Barnsley 2-0 in their replay.
A goal after 34 minutes from Middlesbrough defender Chris Riggott and a penalty six minutes later from Yakubu Aiyegbeni put paid to Nuneaton’s hopes.
The Premier League side scored three more through Stuart Parnaby, a second from Yakubu and Mark Viduka to line up a fourth-round trip to second division Coventry City.
Gez Murphy, who scored the equaliser in the first game, struck twice for Nuneaton.
In the night’s other replay, Cheltenham beat Chester 1-0 and will play Premier League Newcastle United for a place in round five.
Tuesday’s results:
Third round:
Second leg matches:
Birmingham City 2 Torquay United 0
(Birmingham City win on aggregate)
Chester City 0 Cheltenham Town 1
(Cheltenham Town win on aggregate)
Leeds United 3 Wigan Athletic3
(Wigan Athletic win 4-2 on penalties)
Middlesbrough 5 Nuneaton Borough 2
(Middlesbrough win on aggregate)
Reading 3 West Bromwich Albion 2
(Reading win on aggregate)
Tamworth 1 Stoke City 1
( Stoke City win 5-4 on penalties)
Walsall 2 Barnsley 0
(Walsall win on aggregate)
—Reuters