Reid, contracted by West Ham to the end of the 2020-21 season, has not played for the club for almost two years due to injury but may soon earn a recall given the way David Moyes' team are defending.
West Ham were the day's only Premier League team knocked out by a lower-tier club, with West Brom managed by former West Ham boss Slaven Bilic.
Southampton held Tottenham to a 1-1 draw, while Chelsea and Leicester both won.
Sofiane Boufal scored his first goal of the season in the 87th minute to level for Southampton after Son Heung-min had given Tottenham the lead on a swift counter-attack in the 58th minute off Erik Lamela's pass.
The replay will add to Tottenham's troublesome fixture congestion. The North London club needed a replay to beat Middlesbrough in the previous round of the FA Cup.
"It is a result we don't need, we don't need to play one more match, but it is better to play than not to play," said Spurs manager Jose Mourinho.
The replay is likely to be scheduled for February 5, cutting into both teams' time to recover during the Premier League's first winter break.
Mourinho won his first three games after replacing Mauricio Pochettino as Tottenham manager in November but hasn't won back-to-back games since.
Chelsea created enough chances for a big win at Hull City but scraped through only 2-1.
Michy Batshuayi opened the scoring with a deflected shot, and Fikayo Tomori made it 2-0 with a header at a free kick. However, Mason Mount, Pedro and Cesar Azpilicueta all failed to convert good chances, while Hull goalkeeper George Long managed several impressive saves.
Hull forced their way back into the game when Kamil Grosicki's 78th-minute free kick bounced off the Chelsea wall into the top corner of the goal. Grosicki had another chance to level late on but missed.
Leicester City clung on to an early lead after Kelechi Iheanacho's fourth-minute goal to beat Brentford 1-0.
Three touches made Leicester's goal — Dennis Praet's perfectly weighted pass through the defence to the right flank, Marc Albrighton's low cross and Iheanacho's tap-in.
Leicester City manager Brendan Rodgers made nine changes to his line-up, including goalkeeper Danny Ward, who made a good save to keep out Luka Racic's volley late on.
Third-tier Oxford United earned a lucrative replay with Premier League Newcastle after drawing 0-0.
As Reading and Cardiff drew 1-1, there was a warning over Reading's public address system about allegedly racist and homophobic chants by Cardiff fans. It wasn't immediately clear which chants the announcement referred to.
After equalising for Reading, forward Yakou Meite displayed a message on his vest reading "I love you, Papa" and became emotional. Meite posted on Instagram on Wednesday that his father had died.
Sheffield United beat Millwall 2-0, Portsmouth knocked out Barnsley 4-2 and there was a 0-0 draw between Coventry and Birmingham. Coventry was the official home team, though both clubs share the St Andrews stadium in Birmingham.
- AP
