Barcelona's Cristian Tello reacts after scoring against Zaragoza during a Spanish La Liga soccer match at the Romareda stadium in Zaragoza, Spain. AP Photo
The 21-year-old Tello then added another in the 53rd with a brilliant individual effort.
Barcelona increased its lead to 16 points over Real Madrid and Atletico Madrid, which routed Granada 5-0 earlier. Madrid can reclaim sole possession of second place later at Athletic Bilbao.
Messi was left off Barcelona's squad as he recovers from a right hamstring injury that he played through as a substitute to help Barcelona rally against Paris Saint-Germain and reach the Champions League semifinals earlier this week.
The Argentina forward wasn't the only Barcelona player to take the day off.
It played with only five of its regular starters, given that the league title is well in hand and several players need extra rest before its Champions League semifinal with Bayern Munich begins on April 23.
Even with a side full of reserves, Barcelona still had more than enough quality, above all in the playmaking provided by Thiago, to waltz around the relegation-threatened Zaragoza.
Thiago got things rolling by linking up with Alexis Sanchez on the break. He played the Chile forward wide before receiving the ball back and rolling a shot in off the far post before two defenders could close him down.
The 22-year-old midfielder then played Tello through the defense and with time to size up goalkeeper Roberto Jimenez before beating him with a curling left-footed shot.
After Alexis had hit the crossbar, Tello sealed the victory with an audacious step-over dribble to leave defender Glenn Loovens in his tracks before he slipped the ball past Roberto from a tight angle.
Eric Abidal went on in the 78th for Barcelona to a standing ovation from the fans at La Romareda Stadium in his second appearance since returning from a liver transplant.
Zaragoza stayed winless in 2013 and appears destined to yet another late-season struggle to avoid the drop.
Radamel Falcao scored his 23rd and 24th league goals this season to lead Atletico to an easy home victory over Granada.
Diego Costa, Raul Garcia and Filipe Luis netted Atletico's other goals in a game featuring a standout performance by midfielder Jorge "Koke" Resurrecion, who set up three goals with expertly placed free kicks.
Also, Real Sociedad striker Imanol Agirretxe scored two early goals to cement the Basque side's hold on fourth place with a 2-0 victory at Rayo Vallecano.
Sociedad rose four points clear of Malaga and Valencia. It is on a league-best run of just one loss in its last 21 games.