In Montevideo, Liverpool talisman Suarez looked to have earned La Celeste all three points against Paraguay after perfectly connecting with a cross to arrow beyond the goalkeeper.
The Uruguayans conceded with minutes left on the clock, however, and the side who finished fourth at the last World Cup were forced to settle for a 1-1 draw. Sebastian Coates was an unused substitute.
Roy Hodgson's England team cruised to an emphatic 8-0 victory over minnows San Marino in 2014 World Cup qualifying, with in-form Reds striker Sturridge making his mark.
The 23-year-old was introduced on 56 minutes and went close with a header just four minutes after entering the action. He made no mistake with a similar opportunity on 70 minutes, though, to notch his first international strike.
Three Lions captain Steven Gerrard and Reds full-back Glen Johnson were afforded a watching brief tonight ahead of the crunch clash with Group H rivals Montenegro on Tuesday.
Elsewhere, Martin Skrtel wore the captain's armband and played the full 90 minutes as Slovakia came from a goal behind to secure a 1-1 draw at home to Lithuania in Group G.
Daniel Agger enjoyed considerably more success as skipper of Denmark - the centre-back helped his country ease to a 3-0 victory away from home against the Czech Republic.
Reds goalkeeper Pepe Reina watched on from the substitutes' bench as reigning world champions Spain were pegged back to a surprise 1-1 draw with Finland in Gijon.